# cdfst3: Cumulative Distribution Function of the 3-Parameter Student t...

### Description

This function computes the cumulative probability or nonexceedance probability of the 3-parameter Student t distribution given parameters (ξ, α, ν) computed by `parst3`. There is no explicit solution for the cumulative distribution function for value `X` but built-in R functions can be used. For ν ≥ 1000, one can use `pnorm(X, mean=U, sd=A)` for `U` = ξ and `A` = α and for 1.000001 ≤ ν ≤ 1000, one can use `pt((X-U)/A, N)` for `N` = ν and where the R function `pnorm` is for the Normal distribution and the R function `pt` is the 1-parameter Student t distribution.

### Usage

 `1` ```cdfst3(x, para, paracheck=TRUE) ```

### Arguments

 `x` A real value vector. `para` The parameters from `parst3` or `vec2par`. `paracheck` A logical on whether the parameter should be check for validity.

### Value

Nonexceedance probability (F) for x.

W.H. Asquith

### References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

`pdfst3`, `quast3`, `lmomst3`, `parst3`

### Examples

 ```1 2``` ``` lmr <- lmoms(c(123,34,4,654,37,78)) cdfst3(191.5143, parst3(lmr)) # 75th percentile ```

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