Cumulative Density Function of the TPXG Distribution {TPXG}R Documentation

Cumulative Density Function of the TPXG Distribution

Description

Computes the cumulative density function of the Two-Parameter Xgamma distribution for given values.

Usage

ptpxg(x, alpha = 1, theta = 1)

Arguments

x

A numeric vector with strictly positive values.

alpha

A positive real number.

theta

A positive real number.

Details

Let X \sim \text{TPXG}(\alpha,\theta). Then the cumulative distribution function of X is given by:

F(x)=1-\frac{(\alpha+\theta+\alpha \theta x+\frac{1}{2}\alpha \theta^2 x^2)}{(\alpha+\theta)}e^{-\theta x} \quad x,\theta,\alpha > 0

Value

A numeric vector containing the cumulative density function values of the TPXG distribution for each of the given values of x.

Author(s)

Nikolaos Kontemeniotis.

R implementation and documentation: Nikolaos Kontemeniotis kontemeniotisn@gmail.com and Michail Tsagris mtsagris@uoc.gr.

References

"Sen, S., Chandra, N. and Maiti, S. S. (2018). On properties and applications of a two-parameter XGamma distribution. Journal of Statistical Theory and Applications, 17(4): 674–685."

See Also

dtpxg,qtpxg,rtpxg

Examples

x <- ptpxg(100)
ptpxg(x, 1, 1)

[Package TPXG version 1.0 Index]