BayesGOF (version 5.2)

gLP.basis: Determine LP basis functions for prior distribution \(g\)

Description

Determines the LP basis for a given parametric prior distribution.

Usage

gLP.basis(x, g.par, m, con.prior, ind)

Arguments

x

x values (integer or vector) from 0 to 1.

g.par

Estimated parameters for specified prior distribution (i.e beta prior: \(\alpha\) and \(\beta\); normal prior: \(\mu\) and \(\tau^2\); gamma prior: \(\alpha\) and \(\beta\)).

m

Number of LP-Polynomial basis.

con.prior

Specified conjugate prior distribution for basis functions. Options are "Beta", "Normal", and "Gamma".

ind

Default is NULL which returns matrix with \(m\) columns that consists of LP-basis functions; user can provide a specific choice through ind.

Value

Matrix with m columns of values for the LP-Basis functions evaluated at x-values.

References

Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5 .

Mukhopadhyay, S., 2017. "Large-Scale Mode Identification and Data-Driven Sciences," Electronic Journal of Statistics, 11(1), pp.215-240.

Mukhopadhyay, S. and Parzen, E., 2014. "LP Approach to Statistical Modeling," arXiv: 1405.2601.