betapr_flexprob: Conditional probability for Beta Prime distribution

In Shakeel95/bioFlex: Estimation and model selection for strictly positive heavy tailed data, using flexible parametric distributions

Description

betapr_flexprob returns the conditional probability P(Y<k | X) of a model fitted via the function betapr_flexfit; where α has been specified to be a function of covariates the required value should be specified using the ‘features’ parameter. The function includes a procedure for visualizing the conditional probability. betapr_flexprob also allows for the correlation of estimated parameters via the Cholesky decomposition of the variance-covariance matrix.

Usage

betapr_flexprob(K, model, features, visualise = TRUE, draws = 5, xlim)

Arguments

K	Value for which P(Y<k | X) is computed.
model	An object of class "mle2" produced using the function betapr_flexfit.
features	A numeric vector specifying the value of covriates at which the conditional probability should be evaluated; the covariates in the vector should appear in the same order as they do in the model. Where a model does not depend on covariates the argument may be left blank.
visualise	Logical. If TRUE (the default) the conditional distribution is plotted at P(Y<k | x) is shaded.
draws	The number of random draws from multivariate random normal representing correlated parameters. If parameter correlation is not required draws should be set to zero.
xlim	Numeric vectors of length 2, giving the coordinate range of the dependent variable.

Details

This function uses the two parameter parametrization of the Beta Prime distribution is used in Johnson and Kotz (1995). The tow parameter distribution ins a special case of the three parameter distribution, with σ = 1. The probability probability density function is used is:

f(y) = [y^α-1 (1+y)^-(α+β)]/Β(α,β)

The function returns:

P(Y<k | X) = I(α,β)

α may be a function of covariates; in which case, the cannonical log link function is used.

References

Johnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions, Volume 2 (2nd Edition), Wiley.

Shakeel95/bioFlex documentation built on March 3, 2020, 11:27 a.m.