NeuDist (version 1.0.1)

LindleyGIE: Lindley Generalized Inverted Exponential(LGIE) Distribution

Description

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

Usage

dlind.ginv.exp(x, alpha, lambda, theta, log = FALSE)
plind.ginv.exp(q, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
qlind.ginv.exp(p, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
rlind.ginv.exp(n, alpha, lambda, theta)
hlind.ginv.exp(x, alpha, lambda, theta)

Value

• dlind.ginv.exp: numeric vector of (log-)densities

• plind.ginv.exp: numeric vector of probabilities

• qlind.ginv.exp: numeric vector of quantiles

• rlind.ginv.exp: numeric vector of random variates

• hlind.ginv.exp: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

positive numeric parameter

lambda

positive numeric parameter

theta

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 LGIE distribution is parameterized by the parameters \(\alpha > 0\), \(\lambda > 0\), and \(\theta > 0\).

The LGIE distribution has CDF:

$$ F(x; \alpha, \lambda, \theta) = 1-\left(1-e^{-\lambda / x}\right)^{\alpha \theta}\left[1-\left(\frac{\theta} {\theta+1}\right) \ln \left(1-e^{-\lambda / x}\right)^\alpha\right] \quad ;\;x > 0. $$

where \(\alpha\), \(\lambda\), and \(\theta\) are the parameters.

The following functions are included:

• dlind.ginv.exp() — Density function

• plind.ginv.exp() — Distribution function

• qlind.ginv.exp() — Quantile function

• rlind.ginv.exp() — Random generation

• hlind.ginv.exp() — Hazard function

References

Telee, L. B. S., & Kumar, V. (2021). Lindley Generalized Inverted Exponential Distribution: Model and Applications. Pravaha, 27(1), 61--72. tools:::Rd_expr_doi("10.3126/pravaha.v27i1.50616")

Yadav, R.S., & Kumar, V. (2020). Arctan Generalized Inverted Exponential Distribution. J. Nat. Acad. Math., 34, 71--92.

Examples

x <- seq(5, 10, 0.2)
dlind.ginv.exp(x, 5.0, 1.5, 0.5)
plind.ginv.exp(x, 5.0, 1.5, 0.5)
qlind.ginv.exp(0.5, 5.0, 1.5, 0.5)
rlind.ginv.exp(10, 5.0, 1.5, 0.5)
hlind.ginv.exp(x, 5.0, 1.5, 0.5)

# Data
x <- conductors
# ML estimates
params = list(alpha=97.0105, lambda=29.9324, theta=0.9028)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plind.ginv.exp, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dlind.ginv.exp, pfun=plind.ginv.exp, plot=FALSE)
print.gofic(out)