PDF and CDF of t-distribution

gistfile1.txt

# https://www.facebook.com/groups/632755063474501/?multi_permalinks=1910139775736017&notif_id=1542238311570480&notif_t=group_highlights&ref=notif
t.pdf <- function(t,v){
    y <- GAM((v+1)/2)/sqrt(v*pi*GAM(v/2)^2)*(1+t^2/v)^(-(v+1)/2)
    return(y)
}

t.cdf <- function(b,n,t.pdf,v){
    x <- seq(0,b,length=n)[2:(n-1)]
    m <- length(x)
    odd <- seq(1,m,2)
    odd.sum <- 0
    even <- seq(2,m,2)
    even.sum <- 0
    
    for(j in odd) {
        odd.sum <- odd.sum + t.pdf(x[j],v)
    }
    for(k in even){
        even.sum <- even.sum+t.pdf(x[k],v)
    }
    
    i <- (b) * (t.pdf(0,v)+4*odd.sum+2*even.sum+t.pdf(b,v))/(3*n)
    return(round(i,4)+0.5)
}

t.cdf(3,100000,t.pdf,100)

?GAM
??GAM