cTLCAR {TLCAR}

Cumulative Distribution Function (CDF) for the TLCAR Distribution

Description

Calculate the cumulative distribution at a given value using the TLCAR distribution.

Usage

cTLCAR(x, alpha, a, b, theta, m)

Arguments

x

Value at which to calculate the CDF.

alpha

Parameter representing the distribution of the Topp-Leone component.

a

Parameter representing the scale (a) of the Cauchy component.

b

Parameter representing the position (b) of the Cauchy component.

theta

Parameter representing the scale of the Rayleigh component.

m

Additional parameter.

Details

The cumulative distribution function (CDF) for the TLCAR distribution is defined as follows:

F(x)=\left[ 1-\left(\frac{1}{2}-\frac{1}{\pi}\arctan\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right) -b}{a}\right)^2\right]^\alpha

Value

Cumulative distribution at the given value.

Examples

cTLCAR(x = 1, alpha = 1, a = 1, b = 0, theta = 2, m = 0.5)