Tinv
tinv is a statistical function used to compute the inverse cumulative distribution function (quantile) of the Student's t distribution. It returns the t-value corresponding to a given probability for a specified number of degrees of freedom, and is widely used in hypothesis testing and confidence interval construction.
- p is the desired probability in the open interval (0, 1). It represents the cumulative probability
- v is the degrees of freedom, a positive real number.
- tinv(p, v) yields the t such that the CDF of the t distribution with v degrees of
- If p equals 0 or 1, the function typically returns -Inf or Inf, respectively, reflecting the tails
- The function is the inverse of the t distribution CDF (tcdf). It is used to obtain critical
- A common use is t_crit = tinv(1 - alpha/2, v) for a two-sided test at significance level alpha.
- tinv is part of the Statistics and Machine Learning Toolbox in MATLAB, and analogous functions exist
- tinv(0.975, 10) ≈ 2.228, a typical 95% two-tailed critical value for df = 10.
- tinv(0.5, any v) = 0, since the t distribution is symmetric about zero.
- tinv(0.95, 5) ≈ 2.015.
In summary, tinv provides the quantile corresponding to a probability for the Student's t distribution, enabling