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PBI-DataVizzle/pqshared.pq

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Created September 10, 2024 04:44
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pqshared.pq
let
pqmath.Benford =
let
Benford = Function.From(
type function (num as number) as record,
(params) =>
let
len = Text.Length(Text.From(params{0})),
first = if len >= 1 then Number.From(Text.ToList(Text.From(params{0})){0}) else null,
second = if len >= 2 then Number.From(Text.ToList(Text.From(params{0})){1}) else null,
third = if len >= 3 then Number.From(Text.ToList(Text.From(params{0})){2}) else null,
d1 = try Number.Log10(1 + (1 / first)) otherwise null,
d2 = try Number.Log10(1 + (1 / ((10 * first) + second))) otherwise null,
d3 = try Number.Log10(1 + (1 / ((100 * first) + (10 * second) + third))) otherwise null,
return = [Digit_One = d1, Digit_Two = d2, Digit_Three = d3]
in
return
),
fnType = type function (num as number) as record
meta [
Documentation.Name = "pqmath.Benford",
Documentation.LongDescription
= "This provides a Benford analysis for (up to) the first three digits of a number."
]
in
Value.ReplaceType(Benford, fnType),
pqmath.Conf =
let
Conf = Function.From(
type function (z as number, stdev as number, population as number, optional mode as text) as record,
(params) =>
let
// check optional parameter and default to s for sample
m = if params{3} = null then "s" else params{3},
// subtract 1 from population for samples and make that default
n = if m = "p" then params{2} else params{2} - 1,
// calculate output
ci = params{0} * (params{1} / Number.Sqrt(n))
in
[positive = ci, negative = - ci]
),
fnType = type function (
z as number,
stdev as number,
population as number,
optional mode as text
) as record
meta [
Documentation.Name = "pqmath.Conf",
Documentation.LongDescription
= "This takes parameters and provides the confidence interval range.",
Documentation.Examples = {
[
Description
= "Based on z-score, standard deviation, population, and optional mode (""s"" for sample, ""p"" for population), this generates a confidence interval.",
Code = "=pqmath.Conf(1.75, 4, 5000, null)",
Result = "[positive=0.09900485, negative=-0.09900485]"
]
}
]
in
Value.ReplaceType(Conf, fnType),
pqmath.Corr =
let
Corr = Function.From(
type function (t as table) as table,
(params) =>
let
correlation = (x as list, y as list) =>
let
x1 = List.Transform(x, each Number.From(_)),
y1 = List.Transform(y, each Number.From(_)),
sum_x = List.Sum(x1),
sum_y = List.Sum(y1),
sum_x_sq = List.Accumulate(
x1,
0,
(state, current) => Number.From(state) + Number.Power(Number.From(current), 2)
),
sum_y_sq = List.Accumulate(
y1,
0,
(state, current) => Number.From(state) + Number.Power(Number.From(current), 2)
),
sum_xy =
let
l = List.Zip({x1, y1}),
tx = List.Transform(l, each _{0} * _{1}),
sum = List.Sum(tx)
in
sum,
n = List.Count(x1),
r = ((n * sum_xy) - (sum_x * sum_y))
/ Number.Sqrt(
(n * sum_x_sq - Number.Power(sum_x, 2))
* (n * sum_y_sq - Number.Power(sum_y, 2))
)
in
r,
vars = Table.RenameColumns(
Table.TransformColumnTypes(
Table.FromList(
Table.SelectRows(Table.Schema(params{0}), each _[Kind] = "number")[Name]
),
{"Column1", type text}
),
{"Column1", "Vars"}
),
add_vars = Table.AddColumn(vars, "variables", each vars),
expand_vars = Table.ExpandTableColumn(add_vars, "variables", {"Vars"}, {"Vars.1"}),
rename = Table.RenameColumns(expand_vars, {{"Vars", "Var1"}, {"Vars.1", "Var2"}}),
sel = Table.SelectRows(
Table.TransformColumnTypes(rename, {{"Var2", type text}}),
each _[Var1] <> _[Var2]
),
corr = Table.AddColumn(
sel,
"Corr",
each correlation(
Table.ToList(
Table.TransformColumnTypes(
Table.SelectColumns(params{0}, [Var1]),
{[Var1], type text}
)
),
Table.ToList(
Table.TransformColumnTypes(
Table.SelectColumns(params{0}, [Var2]),
{[Var2], type text}
)
)
)
),
sort = Table.Sort(corr, {{"Var1", Order.Ascending}, {"Var2", Order.Ascending}}),
pivot = Table.Pivot(sort, List.Distinct(sort[Var2]), "Var2", "Corr"),
numcols = Table.SelectRows(Table.Schema(pivot), each _[Kind] <> "text")[Name],
types = Table.TransformColumnTypes(
pivot,
List.Zip({numcols, List.Repeat({type number}, List.Count(numcols))})
),
replace_ones = Table.ReplaceValue(types, null, 1, Replacer.ReplaceValue, numcols),
reorder = Table.ReorderColumns(
replace_ones,
List.Combine({{"Var1"}, replace_ones[Var1]})
)
in
reorder
),
fnType = type function (t as table) as table
meta [
Documentation.Name = "pqmath.Corr",
Documentation.LongDescription
= "This function takes a table and generates a Correlation Matrix table.",
Documentation.Examples = {
[
Description = "This provides a correlation matrix based on table t.",
Code = "=pqmath.Corr(Source)",
Result = "Correlation matrix table based on number columns in table passed in."
]
}
]
in
Value.ReplaceType(Corr, fnType),
pqmath.ErlangC =
let
ErlangC = Function.From(
type function (
number_of_calls as number,
period_of_minutes as number,
average_handling_time as number,
required_service_level as number,
target_answer_time as number,
maximum_occupancy as number,
shrinkage as number
) as record,
(params) =>
let
// define probability of waiting function
fnProbWait = (num_agents as number, traffic_intensity as number) =>
let
a_n = Number.Power(traffic_intensity, num_agents),
X = a_n
/ Number.Factorial(num_agents)
* (num_agents / (num_agents - traffic_intensity)),
Y = List.Accumulate(
{0 .. (num_agents - 1)},
0,
(state, current) =>
state + Number.Power(traffic_intensity, current) / Number.Factorial(current)
),
Pw = X / (Y + X)
in
Pw,
// define service level function
fnServiceLevel = (
num_agents as number,
traffic_intensity as number,
prob_waiting as number,
tat as number,
aht as number
) =>
let
ServiceLevel = 1
- (prob_waiting * Number.Exp(- (num_agents - traffic_intensity) * (tat / aht)))
in
ServiceLevel,
// determine calls per hour
calls_per_hour = params{0} * 60 / params{1},
// determine the traffic intensity (A)
A = calls_per_hour * params{2} / 3600,
// determine the number of agents (N) - start with A + 1
N = A + 1,
// raise A to the power of N
A_N = Number.Power(A, N),
// determine the probability of waiting
Pw = fnProbWait(N, A),
// determine the service level
SL = fnServiceLevel(N, A, Pw, params{4}, params{2}),
// iterate until you are N-1 from the target number of agents
Iterate = List.Generate(
() => [Agents = N, Service_Level = SL],
each [Service_Level] < params{3},
each [
Agents = [Agents] + 1,
Service_Level = fnServiceLevel(
[Agents] + 1,
A,
fnProbWait([Agents] + 1, A),
params{4},
params{2}
)
]
),
// figure out N-1 so you can generate the result next
Last = List.LastN(Iterate, 1){0}[Agents],
// generate the result
Output = [
Agents = Last + 1,
Service_Level = fnServiceLevel(
Last + 1,
A,
fnProbWait(Last + 1, A),
params{4},
params{2}
),
Occupancy =
if A / (Last + 1) > params{5} then
A / (A / (Last + 1) / 100)
else
A / (Last + 1),
Shrinkage = (Last + 1) / (1 - (params{6}))
]
in
Output
),
fnType = type function (
number_of_calls as number,
period_of_minutes as number,
average_handling_time as number,
required_service_level as number,
target_answer_time as number,
maximum_occupancy as number,
shrinkage as number
) as record
meta [
Documentation.Name = "pqmath.ErlangC",
Documentation.LongDescription
= "This calculates the probable amount of agents needed to meet the required service level and the probable service level for that number of agents in a record.",
Documentation.Examples = {
[
Description = "This provides an answer for the following parameters: "
& "Number of Calls = 100; "
& "Period of Minutes = 30; "
& "Average Handling Time (Seconds) = 180; "
& "Required Service Level (% expressed as decimal) = .80; "
& "Target Answer Time (Seconds) = 20; ",
Code = "pqmath.ErlangC(100, 30, 180, 0.8, 20)",
Result = "[Agents = 14, Service_Level = 0.888350019]"
]
}
]
in
Value.ReplaceType(ErlangC, fnType),
pqmath.MegaAverage =
let
MegaAverage = Function.From(
type function (l as list) as record,
(params) =>
let
// function for trimmed average
fnGetTrimmed = (lst as list) =>
let
// figure out 1st and 3rd quartiles
Percentile = List.Percentile(
lst,
{0.25, 0.75},
[PercentileMode = PercentileMode.ExcelInc]
),
// get the interquartile range
IQR = Percentile{1} - Percentile{0},
// get the upper limit
Upper = Percentile{1} + (1.5 * IQR),
// get the lower limit
Lower = Percentile{0} - (1.5 * IQR),
// trim outliers
Select = List.Select(lst, each _ < Upper and _ > Lower),
// get the average of the rest
Trimmed = List.Average(Select)
in
Trimmed,
fnGetGeomAvg = // function for the geometric average
(lst as list, n as number) =>
let
// get the natural log of each number
log = List.Transform(lst, each Number.Ln(_)),
// take the average, then apply Number.Exp
log_avg = Number.Exp(List.Sum(log) / n)
in
log_avg,
fnGetWinsorAvg = // function for winsorized average
(lst as list) =>
let
// get the 0.05 and 0.95 percentiles
pcntl = List.Percentile(
lst,
{0.05, 0.95},
[PercentileMode = PercentileMode.ExcelInc]
),
// if the values are outside of these percentiles, replace them
replace = List.Transform(
lst,
each if _ < pcntl{0} then pcntl{0} else if _ > pcntl{1} then pcntl{1} else _
),
// take the average of the list with replacements
winsor_avg = List.Average(replace)
in
winsor_avg,
fnGetHarmonicAvg = // function for harmonic mean
(lst as list, n as number) =>
let
// convert each value to reciprocals
reciprocals = List.Transform(lst, each 1 / _),
// sum the reciprocals
sum_reciprocals = List.Sum(reciprocals),
// divide the sum by the count
harmonic = n / sum_reciprocals
in
harmonic,
// call the functions
count = List.Count(params{0}),
arith = List.Average(params{0}),
med = List.Median(params{0}),
trim = fnGetTrimmed(params{0}),
geom = fnGetGeomAvg(params{0}, count),
wins = fnGetWinsorAvg(params{0}),
harm = fnGetHarmonicAvg(params{0}, count)
in
// return as a record
[
arithmetic = arith,
median = med,
trimmed = trim,
geometric = geom,
winsor = wins,
harmonic = harm,
usage = "Median: Consider when the data is skewed and there are outliers present #(lf)"
& "Trimmed: Consider using when you want to minimize standard error in a dataset with small deviations from normality #(lf)"
& "Geometric: Consider when numbers are positive, exponential, and meant to be multiplied together. Example: Average growth rate, interest rates. #(lf)"
& "Winsor: Consider using when outliers are present and you want to limit their effect #(lf)"
& "Harmonic: Consider using on ratios or fractions, like miles per hour #(lf)"
]
),
fnType = type function (l as list) as record
meta [
Documentation.Name = "pqmath.MegaAverage",
Documentation.LongDescription
= "This function operates on a list and calculates the arithmetic mean, median, trimmed mean, geometric mean, winsorized mean, and harmonic mean.",
Documentation.Examples = {
[
Description = "This provides the different values for an example list.",
Code = "pqmath.MegaAverage({1, 5, 20, 40, 80, 200})",
Result
= "[arithmetic = 57.67, median = 30, trimmed = 29.2, geometric = 20, winsor = 52.83, harmonic= 4.64]"
]
}
]
in
Value.ReplaceType(MegaAverage, fnType),
pqmath.MegaStDevSample =
let
MegaStDevSample = Function.From(
type function (l as list) as record,
(params) =>
let
// function for trimmed average
fnGetTrimmed = (lst as list) =>
let
// figure out 1st and 3rd quartiles
Percentile = List.Percentile(
lst,
{0.25, 0.75},
[PercentileMode = PercentileMode.ExcelInc]
),
// get the interquartile range
IQR = Percentile{1} - Percentile{0},
// get the upper limit
Upper = Percentile{1} + (1.5 * IQR),
// get the lower limit
Lower = Percentile{0} - (1.5 * IQR),
// trim outliers
Select = List.Select(lst, each _ < Upper and _ > Lower),
// get the average of the rest
Trimmed = List.Average(Select)
in
Trimmed,
fnGetGeomAvg = // function for the geometric average
(lst as list, n as number) =>
let
// get the natural log of each number
log = List.Transform(lst, each Number.Ln(_)),
// take the average, then apply Number.Exp
log_avg = Number.Exp(List.Sum(log) / n)
in
log_avg,
fnGetWinsorAvg = // function for winsorized average
(lst as list) =>
let
// get the 0.05 and 0.95 percentiles
pcntl = List.Percentile(
lst,
{0.05, 0.95},
[PercentileMode = PercentileMode.ExcelInc]
),
// if the values are outside of these percentiles, replace them
replace = List.Transform(
lst,
each if _ < pcntl{0} then pcntl{0} else if _ > pcntl{1} then pcntl{1} else _
),
// take the average of the list with replacements
winsor_avg = List.Average(replace)
in
winsor_avg,
fnGetHarmonicAvg = // function for harmonic mean
(lst as list, n as number) =>
let
// convert each value to reciprocals
reciprocals = List.Transform(lst, each 1 / _),
// sum the reciprocals
sum_reciprocals = List.Sum(reciprocals),
// divide the sum by the count
harmonic = n / sum_reciprocals
in
harmonic,
fnStDevSample = // function to manually calculate the standard deviation for a sample population
(lst as list, rcd as text, degrees as number) =>
let
stdev = Number.Sqrt(
List.Sum(List.Transform(lst, each Record.Field(_, rcd))) / degrees
)
in
stdev,
// call the functions
count = List.Count(params{0}),
arith = List.Average(params{0}),
trim = fnGetTrimmed(params{0}),
geom = fnGetGeomAvg(params{0}, count),
wins = fnGetWinsorAvg(params{0}),
harm = fnGetHarmonicAvg(params{0}, count),
dof = count - 1,
loop = List.Generate(
() => [
i = 0,
a = Number.Power(params{0}{0} - arith, 2),
t = Number.Power(params{0}{0} - trim, 2),
g = Number.Power(params{0}{0} - geom, 2),
w = Number.Power(params{0}{0} - wins, 2),
h = Number.Power(params{0}{0} - harm, 2)
],
each [i] <= dof,
each [
i = [i] + 1,
a = Number.Power(params{0}{[i] + 1} - arith, 2),
t = Number.Power(params{0}{[i] + 1} - trim, 2),
g = Number.Power(params{0}{[i] + 1} - geom, 2),
w = Number.Power(params{0}{[i] + 1} - wins, 2),
h = Number.Power(params{0}{[i] + 1} - harm, 2)
]
)
in
// return as a record
[
arithmetic = List.StandardDeviation(params{0}),
trimmed = fnStDevSample(loop, "t", dof),
geometric = fnStDevSample(loop, "g", dof),
winsor = fnStDevSample(loop, "w", dof),
harmonic = fnStDevSample(loop, "h", dof),
usage = "Arithmetic: Standard deviation for sample population based on arithmetic mean #(lf)"
& "Trimmed: Consider using when you want to minimize standard error in a dataset with small deviations from normality #(lf)"
& "Geometric: Consider when numbers are positive, exponential, and meant to be multiplied together. Example: Average growth rate, interest rates. #(lf)"
& "Winsor: Consider using when outliers are present and you want to limit their effect #(lf)"
& "Harmonic: Consider using on ratios or fractions, like miles per hour #(lf)"
]
),
fnType = type function (l as list) as record
meta [
Documentation.Name = "pqmath.MegaStDevSample",
Documentation.LongDescription
= "This function operates on a list and calculates different means and uses those means as part of a sample standard deviation calculation.",
Documentation.Examples = {
[
Description = "This provides the different values for an example list.",
Code = "= pqmath.MegaStDevSample({1, 5, 10, 20, 22})",
Result
= "[arithmetic = 9.18, trimmed = 9.18, geometric = 10.32, winsor = 9.18, harmonic= 12.83]"
]
}
]
in
Value.ReplaceType(MegaStDevSample, fnType),
pqmath.QuartileStats =
let
QuartileStats = Function.From(
type function (val as number, col as list) as record,
(params) =>
let
l = List.Sort(params{1}),
count = List.Count(l),
q1 = count * 0.25,
q2 = count * 0.5,
q3 = count * 0.75,
fnRunCheck = (check as number) =>
let
get_q =
if check = Number.IntegerDivide(check, 1) then
List.Average({l{Number.Round(check, 0) - 1}, l{Number.Round(check, 0)}})
else
l{Number.Round(check, 0)}
in
get_q,
q1_val = fnRunCheck(q1),
q2_val = fnRunCheck(q2),
q3_val = fnRunCheck(q3),
iqr = q3_val - q1_val,
return = [
quartile =
if params{0} <= q1_val then
1
else if params{0} <= q2_val then
2
else if params{0} <= q3_val then
3
else
4,
q1 = q1_val,
q2 = q2_val,
q3 = q3_val,
interquartile_range = iqr,
outlier =
if params{0} < q1_val - (1.5 * iqr) then
true
else if params{0} > q3_val + (1.5 * iqr) then
true
else
false
]
in
return
),
fnType = type function (val as number, col as list) as record
meta [
Documentation.Name = "pqmath.QuartileStats",
Documentation.LongDescription
= "This provides quartiles and whether a row value is an outlier based on a column of data/list."
]
in
Value.ReplaceType(QuartileStats, fnType),
pqmath.Z =
let
Z = Function.From(
type function (test_type as text, value as number) as record,
(params) =>
let
// define z table - taken from https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf
standard = Table.FromRecords(
{
[z = - 3.99, area_left = 0.00003, area_right = 0.99997, position = "below mean"],
[z = - 3.98, area_left = 0.00003, area_right = 0.99997, position = "below mean"],
[z = - 3.97, area_left = 0.00004, area_right = 0.99996, position = "below mean"],
[z = - 3.96, area_left = 0.00004, area_right = 0.99996, position = "below mean"],
[z = - 3.95, area_left = 0.00004, area_right = 0.99996, position = "below mean"],
[z = - 3.94, area_left = 0.00004, area_right = 0.99996, position = "below mean"],
[z = - 3.93, area_left = 0.00004, area_right = 0.99996, position = "below mean"],
[z = - 3.92, area_left = 0.00004, area_right = 0.99996, position = "below mean"],
[z = - 3.91, area_left = 0.00005, area_right = 0.99995, position = "below mean"],
[z = - 3.9, area_left = 0.00005, area_right = 0.99995, position = "below mean"],
[z = - 3.89, area_left = 0.00005, area_right = 0.99995, position = "below mean"],
[z = - 3.88, area_left = 0.00005, area_right = 0.99995, position = "below mean"],
[z = - 3.87, area_left = 0.00005, area_right = 0.99995, position = "below mean"],
[z = - 3.86, area_left = 0.00006, area_right = 0.99994, position = "below mean"],
[z = - 3.85, area_left = 0.00006, area_right = 0.99994, position = "below mean"],
[z = - 3.84, area_left = 0.00006, area_right = 0.99994, position = "below mean"],
[z = - 3.83, area_left = 0.00006, area_right = 0.99994, position = "below mean"],
[z = - 3.82, area_left = 0.00007, area_right = 0.99993, position = "below mean"],
[z = - 3.81, area_left = 0.00007, area_right = 0.99993, position = "below mean"],
[z = - 3.8, area_left = 0.00007, area_right = 0.99993, position = "below mean"],
[z = - 3.79, area_left = 0.00008, area_right = 0.99992, position = "below mean"],
[z = - 3.78, area_left = 0.00008, area_right = 0.99992, position = "below mean"],
[z = - 3.77, area_left = 0.00008, area_right = 0.99992, position = "below mean"],
[z = - 3.76, area_left = 0.00008, area_right = 0.99992, position = "below mean"],
[z = - 3.75, area_left = 0.00009, area_right = 0.99991, position = "below mean"],
[z = - 3.74, area_left = 0.00009, area_right = 0.99991, position = "below mean"],
[z = - 3.73, area_left = 0.0001, area_right = 0.9999, position = "below mean"],
[z = - 3.72, area_left = 0.0001, area_right = 0.9999, position = "below mean"],
[z = - 3.71, area_left = 0.0001, area_right = 0.9999, position = "below mean"],
[z = - 3.7, area_left = 0.00011, area_right = 0.99989, position = "below mean"],
[z = - 3.69, area_left = 0.00011, area_right = 0.99989, position = "below mean"],
[z = - 3.68, area_left = 0.00012, area_right = 0.99988, position = "below mean"],
[z = - 3.67, area_left = 0.00012, area_right = 0.99988, position = "below mean"],
[z = - 3.66, area_left = 0.00013, area_right = 0.99987, position = "below mean"],
[z = - 3.65, area_left = 0.00013, area_right = 0.99987, position = "below mean"],
[z = - 3.64, area_left = 0.00014, area_right = 0.99986, position = "below mean"],
[z = - 3.63, area_left = 0.00014, area_right = 0.99986, position = "below mean"],
[z = - 3.62, area_left = 0.00015, area_right = 0.99985, position = "below mean"],
[z = - 3.61, area_left = 0.00015, area_right = 0.99985, position = "below mean"],
[z = - 3.6, area_left = 0.00016, area_right = 0.99984, position = "below mean"],
[z = - 3.59, area_left = 0.00017, area_right = 0.99983, position = "below mean"],
[z = - 3.58, area_left = 0.00017, area_right = 0.99983, position = "below mean"],
[z = - 3.57, area_left = 0.00018, area_right = 0.99982, position = "below mean"],
[z = - 3.56, area_left = 0.00019, area_right = 0.99981, position = "below mean"],
[z = - 3.55, area_left = 0.00019, area_right = 0.99981, position = "below mean"],
[z = - 3.54, area_left = 0.0002, area_right = 0.9998, position = "below mean"],
[z = - 3.53, area_left = 0.00021, area_right = 0.99979, position = "below mean"],
[z = - 3.52, area_left = 0.00022, area_right = 0.99978, position = "below mean"],
[z = - 3.51, area_left = 0.00022, area_right = 0.99978, position = "below mean"],
[z = - 3.5, area_left = 0.00023, area_right = 0.99977, position = "below mean"],
[z = - 3.49, area_left = 0.00024, area_right = 0.99976, position = "below mean"],
[z = - 3.48, area_left = 0.00025, area_right = 0.99975, position = "below mean"],
[z = - 3.47, area_left = 0.00026, area_right = 0.99974, position = "below mean"],
[z = - 3.46, area_left = 0.00027, area_right = 0.99973, position = "below mean"],
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z = 2.19,
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z = 2.22,
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z = 2.27,
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z = 2.33,
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z = 2.34,
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z = 2.35,
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z = 2.36,
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z = 2.37,
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z = 2.39,
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z = 2.4,
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z = 2.41,
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z = 2.42,
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z = 2.43,
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z = 2.44,
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z = 2.45,
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z = 2.46,
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z = 2.47,
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z = 2.48,
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z = 2.49,
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z = 2.5,
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z = 2.51,
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z = 2.52,
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z = 2.53,
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z = 2.54,
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z = 2.55,
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z = 2.56,
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z = 2.57,
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z = 2.58,
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z = 2.59,
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z = 2.61,
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z = 2.62,
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z = 2.64,
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z = 2.65,
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z = 2.66,
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z = 2.67,
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z = 2.68,
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z = 2.69,
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z = 2.7,
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z = 2.71,
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z = 2.72,
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z = 2.73,
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z = 2.74,
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z = 2.75,
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z = 2.76,
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z = 2.77,
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z = 2.78,
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z = 2.79,
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z = 2.8,
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z = 2.81,
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z = 2.82,
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z = 2.83,
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z = 2.84,
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z = 2.85,
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z = 2.86,
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z = 2.88,
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z = 2.89,
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z = 2.9,
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z = 2.91,
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z = 2.92,
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z = 2.93,
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z = 2.94,
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z = 2.95,
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z = 2.96,
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z = 2.97,
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z = 3,
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z = 3.01,
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z = 3.02,
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z = 3.04,
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z = 3.05,
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z = 3.06,
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z = 3.07,
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z = 3.08,
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z = 3.1,
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z = 3.11,
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z = 3.12,
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z = 3.13,
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z = 3.14,
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z = 3.15,
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z = 3.16,
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z = 3.17,
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z = 3.18,
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z = 3.19,
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z = 3.2,
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z = 3.21,
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z = 3.22,
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z = 3.23,
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z = 3.24,
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area_right = 0.000600000000000045,
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z = 3.25,
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z = 3.26,
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z = 3.27,
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z = 3.28,
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z = 3.29,
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area_right = 0.000499999999999945,
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z = 3.3,
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z = 3.31,
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area_right = 0.00046999999999997,
position = "above mean"
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z = 3.32,
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area_right = 0.00044999999999995,
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z = 3.33,
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area_right = 0.000430000000000041,
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z = 3.34,
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area_right = 0.000419999999999976,
position = "above mean"
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z = 3.35,
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area_right = 0.000399999999999956,
position = "above mean"
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z = 3.36,
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area_right = 0.000390000000000001,
position = "above mean"
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z = 3.37,
area_left = 0.99962,
area_right = 0.000380000000000047,
position = "above mean"
],
[
z = 3.38,
area_left = 0.99964,
area_right = 0.000360000000000027,
position = "above mean"
],
[
z = 3.39,
area_left = 0.99965,
area_right = 0.000349999999999961,
position = "above mean"
],
[
z = 3.4,
area_left = 0.99966,
area_right = 0.000340000000000007,
position = "above mean"
],
[
z = 3.41,
area_left = 0.99968,
area_right = 0.000319999999999987,
position = "above mean"
],
[
z = 3.42,
area_left = 0.99969,
area_right = 0.000310000000000032,
position = "above mean"
],
[
z = 3.43,
area_left = 0.9997,
area_right = 0.000299999999999967,
position = "above mean"
],
[
z = 3.44,
area_left = 0.99971,
area_right = 0.000290000000000012,
position = "above mean"
],
[
z = 3.45,
area_left = 0.99972,
area_right = 0.000279999999999947,
position = "above mean"
],
[
z = 3.46,
area_left = 0.99973,
area_right = 0.000269999999999992,
position = "above mean"
],
[
z = 3.47,
area_left = 0.99974,
area_right = 0.000260000000000038,
position = "above mean"
],
[
z = 3.48,
area_left = 0.99975,
area_right = 0.000249999999999972,
position = "above mean"
],
[
z = 3.49,
area_left = 0.99976,
area_right = 0.000240000000000018,
position = "above mean"
],
[
z = 3.5,
area_left = 0.99977,
area_right = 0.000229999999999952,
position = "above mean"
],
[
z = 3.51,
area_left = 0.99978,
area_right = 0.000219999999999998,
position = "above mean"
],
[
z = 3.52,
area_left = 0.99978,
area_right = 0.000219999999999998,
position = "above mean"
],
[
z = 3.53,
area_left = 0.99979,
area_right = 0.000210000000000043,
position = "above mean"
],
[
z = 3.54,
area_left = 0.9998,
area_right = 0.000199999999999978,
position = "above mean"
],
[
z = 3.55,
area_left = 0.99981,
area_right = 0.000190000000000023,
position = "above mean"
],
[
z = 3.56,
area_left = 0.99981,
area_right = 0.000190000000000023,
position = "above mean"
],
[
z = 3.57,
area_left = 0.99982,
area_right = 0.000179999999999958,
position = "above mean"
],
[
z = 3.58,
area_left = 0.99983,
area_right = 0.000170000000000003,
position = "above mean"
],
[
z = 3.59,
area_left = 0.99983,
area_right = 0.000170000000000003,
position = "above mean"
],
[
z = 3.6,
area_left = 0.99984,
area_right = 0.000160000000000049,
position = "above mean"
],
[
z = 3.61,
area_left = 0.99985,
area_right = 0.000149999999999983,
position = "above mean"
],
[
z = 3.62,
area_left = 0.99985,
area_right = 0.000149999999999983,
position = "above mean"
],
[
z = 3.63,
area_left = 0.99986,
area_right = 0.000140000000000029,
position = "above mean"
],
[
z = 3.64,
area_left = 0.99986,
area_right = 0.000140000000000029,
position = "above mean"
],
[
z = 3.65,
area_left = 0.99987,
area_right = 0.000129999999999963,
position = "above mean"
],
[
z = 3.66,
area_left = 0.99987,
area_right = 0.000129999999999963,
position = "above mean"
],
[
z = 3.67,
area_left = 0.99988,
area_right = 0.000120000000000009,
position = "above mean"
],
[
z = 3.68,
area_left = 0.99988,
area_right = 0.000120000000000009,
position = "above mean"
],
[
z = 3.69,
area_left = 0.99989,
area_right = 0.000110000000000054,
position = "above mean"
],
[
z = 3.7,
area_left = 0.99989,
area_right = 0.000110000000000054,
position = "above mean"
],
[
z = 3.71,
area_left = 0.9999,
area_right = 0.000099999999999989,
position = "above mean"
],
[
z = 3.72,
area_left = 0.9999,
area_right = 0.000099999999999989,
position = "above mean"
],
[
z = 3.73,
area_left = 0.9999,
area_right = 0.000099999999999989,
position = "above mean"
],
[
z = 3.74,
area_left = 0.99991,
area_right = 9.00000000000345E-05,
position = "above mean"
],
[
z = 3.75,
area_left = 0.99991,
area_right = 9.00000000000345E-05,
position = "above mean"
],
[
z = 3.76,
area_left = 0.99992,
area_right = 0.000079999999999969,
position = "above mean"
],
[
z = 3.77,
area_left = 0.99992,
area_right = 0.000079999999999969,
position = "above mean"
],
[
z = 3.78,
area_left = 0.99992,
area_right = 0.000079999999999969,
position = "above mean"
],
[
z = 3.79,
area_left = 0.99992,
area_right = 0.000079999999999969,
position = "above mean"
],
[
z = 3.8,
area_left = 0.99993,
area_right = 7.00000000000145E-05,
position = "above mean"
],
[
z = 3.81,
area_left = 0.99993,
area_right = 7.00000000000145E-05,
position = "above mean"
],
[
z = 3.82,
area_left = 0.99993,
area_right = 7.00000000000145E-05,
position = "above mean"
],
[
z = 3.83,
area_left = 0.99994,
area_right = 0.000059999999999949,
position = "above mean"
],
[
z = 3.84,
area_left = 0.99994,
area_right = 0.000059999999999949,
position = "above mean"
],
[
z = 3.85,
area_left = 0.99994,
area_right = 0.000059999999999949,
position = "above mean"
],
[
z = 3.86,
area_left = 0.99994,
area_right = 0.000059999999999949,
position = "above mean"
],
[
z = 3.87,
area_left = 0.99995,
area_right = 4.99999999999945E-05,
position = "above mean"
],
[
z = 3.88,
area_left = 0.99995,
area_right = 4.99999999999945E-05,
position = "above mean"
],
[
z = 3.89,
area_left = 0.99995,
area_right = 4.99999999999945E-05,
position = "above mean"
],
[
z = 3.9,
area_left = 0.99995,
area_right = 4.99999999999945E-05,
position = "above mean"
],
[
z = 3.91,
area_left = 0.99995,
area_right = 4.99999999999945E-05,
position = "above mean"
],
[
z = 3.92,
area_left = 0.99996,
area_right = 0.00004000000000004,
position = "above mean"
],
[
z = 3.93,
area_left = 0.99996,
area_right = 0.00004000000000004,
position = "above mean"
],
[
z = 3.94,
area_left = 0.99996,
area_right = 0.00004000000000004,
position = "above mean"
],
[
z = 3.95,
area_left = 0.99996,
area_right = 0.00004000000000004,
position = "above mean"
],
[
z = 3.96,
area_left = 0.99996,
area_right = 0.00004000000000004,
position = "above mean"
],
[
z = 3.97,
area_left = 0.99996,
area_right = 0.00004000000000004,
position = "above mean"
],
[
z = 3.98,
area_left = 0.99997,
area_right = 2.99999999999745E-05,
position = "above mean"
],
[
z = 3.99,
area_left = 0.99997,
area_right = 2.99999999999745E-05,
position = "above mean"
]
},
type table [z = number, area_left = number, area_right = number, position = text]
),
// check the test type, if it is not z, subtract from 1
v = if params{0} <> "z" then Number.Round(1 - params{1}, 3) else params{1},
get_values = // lookup values based on test - default to z lookup
if params{0} = "r" then
Table.ToRecords(
Table.LastN(Table.SelectRows(standard, each Number.Round([area_right], 3) = v), 1)
)
else if params{0} = "l" then
Table.ToRecords(
Table.FirstN(Table.SelectRows(standard, each Number.Round([area_left], 3) = v), 1)
)
else if params{0} = "t" then
Table.SelectRows(
standard,
each Number.Round([area_left], 3)
= Number.Round(v / 2, 3)
or Number.Round([area_right], 3) = Number.Round(v / 2, 3)
)
else
Table.SelectRows(standard, each [z] = v)
in
get_values
),
fnType = type function (test_type as text, value as number) as record
meta [
Documentation.Name = "pqstat.Z",
Documentation.LongDescription = "This provides lookup capabilities on the Standard Table for Z Scores. "
& "The second value is either the confidence level you are looking for or the z-score you are looking up.",
Documentation.Examples = {
[
Description = "The test types can be the following: "
& "t = two-tailed test; "
& "l = left-tailed test; "
& "r = right-tailed test; "
& "z = lookup based on z score",
Code = "fnZTable(""r"", 0.95)",
Result = "[z=1.64, area_left = 0.9495, area_right=0.0505, position= above mean]"
]
}
]
in
Value.ReplaceType(Z, fnType),
return = Table.FromRecords(
{
[Name = "pqmath.Benford", Function = pqmath.Benford],
[Name = "pqmath.Conf", Function = pqmath.Conf],
[Name = "pqmath.Corr", Function = pqmath.Corr],
[Name = "pqmath.ErlangC", Function = pqmath.ErlangC],
[Name = "pqmath.MegaAverage", Function = pqmath.MegaAverage],
[Name = "pqmath.MegaStDevSample", Function = pqmath.MegaStDevSample],
[Name = "pqmath.QuartileStats", Function = pqmath.QuartileStats],
[Name = "pqmath.Z", Function = pqmath.Z]
},
type table [Name = Text.Type, Function = Function.Type]
)
in
return
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