Student's t cumulative distribution function
p = tcdf(x,nu)
p = tcdf(x,nu,'upper')
p = tcdf(x,nu) returns the cumulative distribution function (cdf) of the Student's t distribution at each of the values in x using the corresponding degrees of freedom in nu. x and nu can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs.
p = tcdf(x,nu,'upper') returns the complement of the Student's t cdf at each value in x, using an algorithm that more accurately computes the extreme upper tail probabilities.
mu = 1; % Population mean sigma = 2; % Population standard deviation n = 100; % Sample size rng default % For reproducibility x = normrnd(mu,sigma,n,1); % Random sample from population xbar = mean(x); % Sample mean s = std(x); % Sample standard deviation t = (xbar - mu)/(s/sqrt(n))
t = 1.0589
p = 1-tcdf(t,n-1) % Probability of larger t-statistic
p = 0.1461
This probability is the same as the p value returned by a t test of the null hypothesis that the sample comes from a normal population with mean
[h,ptest] = ttest(x,mu,0.05,'right')
h = 0 ptest = 0.1461
The cumulative distribution function (cdf) of Student's t distribution is
where ν is the degrees of freedom and Γ( · ) is the Gamma function. The result p is the probability that a single observation from the t distribution with ν degrees of freedom will fall in the interval [–∞, x].