NeuDist (version 1.0.1)

Perks: Perks Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Perks distribution.

Usage

dperks(x, alpha, beta, log = FALSE)
pperks(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qperks(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
rperks(n, alpha, beta)
hperks(x, alpha, beta)
dperks(x, alpha, beta, log = FALSE)
pperks(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qperks(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
rperks(n, alpha, beta)
hperks(x, alpha, beta)

Value

• dperks: numeric vector of (log-)densities

• pperks: numeric vector of probabilities

• qperks: numeric vector of quantiles

• rperks: numeric vector of random variates

• hperks: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

positive numeric parameter

beta

positive numeric parameter

log

logical; if TRUE, returns log-density

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).

log.p

logical; if TRUE, probabilities are given as log(p)

p

numeric vector of probabilities (0 < p < 1)

n

number of observations (integer > 0)

Details

The Perks distribution is parameterized by the parameters \(\alpha > 0\) and \(\beta > 0\).

The Perks distribution has CDF:

$$ F(x; \alpha, \beta) = \quad 1 - \left( {\frac{{1 + \alpha }}{{1 + \alpha {e^{\beta x}}}}} \right) \, ; \quad x \ge 0. $$

where \(\alpha\) and \(\beta\) are the parameters.

The following functions are included:

• dperks() — Density function

• pperks() — Distribution function

• qperks() — Quantile function

• rperks() — Random generation

• hperks() — Hazard function

References

Richards, S.J. (2008). Applying survival models to pensioner mortality data. Bra. Actuarial Journal, 14, 257--303.

Chaudhary, A.K., & Kumar, V. (2013). A Bayesian Analysis of Perks Distribution via Markov Chain Monte Carlo Simulation. Nepal Journal of Science and Technology, 14(1), 153--166. tools:::Rd_expr_doi("10.3126/njst.v14i1.8936")

Richards, S. J. (2012). A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal, 1--25.

Examples

x <- seq(0.1, 2.0, 0.1)
dperks(x, 5.0, 1.5)
pperks(x, 5.0, 1.5)
qperks(0.5, 5.0, 1.5)
rperks(10, 5.0, 1.5)
hperks(x, 5.0, 1.5)

# Data
x <- conductors
# ML estimates
params = list(alpha=4.5967e-4, beta=1.1077)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pperks, fit.line=TRUE)

#Q-Q (quantile–quantile) plot 
qq.plot(x, params = params, qfun = qperks, fit.line=TRUE)

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dperks, pfun=pperks, plot=TRUE)
print.gofic(out)