CBXBio function

Complementary Burr-X binomial distribution

Evaluates the PDF, CDF, QF, random numbers and MLEs based on the complementary Burr-X binomial (CBXBio) distribution. The CDF of the complementary G binomial distribution is as follows: [REMOVE_ME]$F(x)=\frac{\left[1-\lambda(1-G(x))\right]^{m}-(1-\lambda)^{m}}{1-(1-\lambda)^{m}};\qquad\lambda\in\left(0,1\right),\,m\geq1, [REMOVE_ME_2]$

where G(x) represents the baseline Burr-X CDF, it is given by [REMOVE_ME]$G(x)=\left[1-\exp\left(-x^{2}\right)\right]^{a};\qquad a>0. [REMOVE_ME_2]$

By setting G(x) in the above Equation, yields the CDF of the CBXBio distribution.

Description

Evaluates the PDF, CDF, QF, random numbers and MLEs based on the complementary Burr-X binomial (CBXBio) distribution. The CDF of the complementary G binomial distribution is as follows:

where G(x) represents the baseline Burr-X CDF, it is given by

By setting G(x) in the above Equation, yields the CDF of the CBXBio distribution.

dCBXBio(x, a, m, lambda, log = FALSE)
pCBXBio(x, a, m, lambda, log.p = FALSE, lower.tail = TRUE)
qCBXBio(p, a, m, lambda, log.p = FALSE, lower.tail = TRUE)
rCBXBio(n, a, m, lambda)
mCBXBio(x, a, m, lambda, method="B")

Arguments

• x: A vector of (non-negative integer) quantiles.
• p: A vector of probablities.
• n: The number of random values to be generated under the CBXBio distribution.
• lambda: The strictly positive parameter of the binomial distribution $\lambda \in (0,1)$.
• m: The positive parameter of the binomial distribution $m \geq 1$.
• a: The strictly positive shape parameter of the baseline Burr-X distribution ($a > 0$).
• lower.tail: if FALSE then 1-F(x) are returned and quantiles are computed 1-p.
• log: if TRUE, probabilities p are given as log(p).
• log.p: if TRUE, probabilities p are given for exp(p).
• method: the procedure for optimizing the log-likelihood function after setting the intial values of the parameters and data values for which the CBXBio distribution is fitted. It could be "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", or "SANN". "BFGS" is set as the default.

Details

These functions allow for the evaluation of the PDF, CDF, QF, random numbers and MLEs of the unknown parameters with the standard error (SE) of the estimates of the CBXBio distribution. Additionally, it offers goodness-of-fit statistics such as the AIC, BIC, -2L, A test, W test, Kolmogorov-Smirnov test, P-value, and convergence status.

Returns

dCBXBio gives the (log) probability function. pCBXBio gives the (log) distribution function. qCBXBio gives the quantile function. rCBXBio generates random values. mCBXBio gives the estimated parameters along with SE and goodness-of-fit measures.

References

Tahir, M. H., & Cordeiro, G. M. (2016). Compounding of distributions: a survey and new generalized classes. Journal of Statistical Distributions and Applications, 3, 1-35.

Kleiber, C., & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences. John Wiley & Sons.

Author(s)

Muhammad Imran and M.H Tahir.

R implementation and documentation: Muhammad Imran imranshakoor84@yahoo.com and M.H Tahir mht@iub.edu.pk .

See Also

dCB12Geo

Examples

x<-data_guineapigs
dCBXBio(x,2,2,0.3)
pCBXBio(x,2,2,0.4)
qCBXBio(0.7,2,2,0.7)
mCBXBio(x,0.2,2,0.3, method="B")