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