# 3.5.3.1.23 Tcdf

## Description

Computes the probabilities of the specified tail type tail, associated with a cumulative distribution function of Student's t-distribution with the degree of freedom df.

## Syntax

double prob = tcdf(double t, double df[, int tail])

## Parameters

t

Input, the value of the Student's $t$ variate.[$-\infty,+\infty$]

df

Input, the degrees of freedom, $\nu$ , of the Student's t-distribution.($df\geq 1$)

tail

Input, Optional. The tail probability type using for the Student's t-distribution
• 1 = the for upper tail probability
• 2 = the lower tail probability (Default if not set)
• 3 = the two tail (significance level) probability
• 4 = the two tail (confidence interval) probability

prob

Output, the probability.

## Example

tcdf(38.9036068506926,30, 3)=;     // ANS: 3.110454711125E-27