BBUM_distribution: Bi-beta-uniform mixture (BBUM) distribution

In wyppeter/bbum: BBUM correction for significance testing of p values

Bi-beta-uniform mixture (BBUM) distribution

Description

Density, distribution function, and random generation for the BBUM distribution, with four parameters, lambda, a, theta, and r. The quantile function cannot be simply expressed and is thus not available.

Usage

dbbum(x, lambda, a, theta, r)

pbbum(q, lambda, a, theta, r)

rbbum(n, lambda, a, theta, r)

rbbum.ID(n, lambda, a, theta, r)

Arguments

x	Vector of quantiles.
lambda	Vector of BBUM parameter lambda. lambda is the fraction of null (uniform distribution density) over all density except the primary beta distribution, i.e. null plus secondary beta.
a	Vector of BBUM parameter a, which corresponds to the a shape parameter of the secondary beta distribution component. It describes the steepness of the second beta distribution.
theta	Vector of BBUM parameter theta. theta is the fraction of primary beta distribution density over all density.
r	Vector of BBUM parameter r, which is the ratio of the a shape parameter of the primary beta distribution over that of the secondary beta distribution. In other words, a*r is the shape parameter for the primary beta distribution component.
q	Vector of quantiles.
n	Number of observations.

Details

The b parameter of the typical beta distribution function is constrained to be 1 here to limit it to a one-sided, monotonic case, peaking at 0, when 0 < a < 1.

Value

dbbum gives the density (PDF), and pbbum gives the distribution function (CDF). rbbum generates random values from the distribution, and rbbum.ID generates random values while identifying the part of BBUM they belong to, as a data.frame of two columns with length n. pvalue corresponds to the generated values, while cate is 0 for null, 1 for primary beta, and 2 for secondary beta.

Examples

dbbum(x = 0.096, lambda = 0.65, a = 0.1, theta = 0.02, r = 0.07)
pbbum(q = 0.096, lambda = 0.65, a = 0.1, theta = 0.02, r = 0.07)

dbbum(x = c(0.013, 0.04, 0.93, 0.8), lambda = 0.73, a = 0.02, theta = 0.11, r = 0.003)
pbbum(q = c(0.013, 0.04, 0.93, 0.8), lambda = 0.73, a = 0.02, theta = 0.11, r = 0.003)

rbbum(n = 100, lambda = 0.65, a = 0.1, theta = 0.02, r = 0.07)

rbbum.ID(n = 100, lambda = 0.65, a = 0.1, theta = 0.02, r = 0.07)

wyppeter/bbum documentation built on Oct. 3, 2023, 3:29 p.m.