A New Truncated Lindley-Generated Family of Distributions: Properties, Regression Analysis, and Applications

Abstract

We present the truncated Lindley-G (TLG) model, a novel class of probability distributions with an additional shape parameter, by composing a unit distribution called the truncated Lindley distribution with a parent distribution function G(x). The proposed model's characteristics including critical points, moments, generating function, quantile function, mean deviations, and entropy are discussed. Also, we introduce a regression model based on the truncated Lindley-Weibull distribution considering two systematic components. The model parameters are estimated using the maximum likelihood method. In order to investigate the behavior of the estimators, some simulations are run for various parameter settings, censoring percentages, and sample sizes. Four real datasets are used to demonstrate the new model's potential.

Keywords: COVID-19 data; censored data; maximum likelihood; regression model; survival function.

Figure 1

The pdf of the TLW model.

Figure 2

Regions of the Cartesian plane $\theta {\tau }^{*}$ where different forms of the TLW pdf occur.

Figure 3

Histogram and fitted pdf, empirical and fitted cdfs, and P–P and Q–Q plots of the TLW model fitted to dataset I.

Figure 4

Histogram and fitted pdf, empirical and fitted cdfs, and P–P and Q–Q plots of the TLW model fitted to dataset II.

Figure 5

(a) Kaplan–Meier survival curve for the sex variable ($1=$ male, $0=$ female); (b) histogram of the age variable.

Figure 6

Index plot and normal probability plot with envelope of the deviance residual from the fitted regressions model to the COVID-19 data. (a,b): ${\mathcal{M}}_3$-TLW; (c,d): ${\mathcal{M}}_3$-Weibull.

Figure 7

Kaplan–Meier survival curve and estimated survival functions from the ${\mathcal{M}}_3$-TLW by sex.

Figure 8

Boxplot of colors by class for the Post-harvested dataset.

Figure 9

Index plot, normal probability plot with envelope, and worm plot of the quantile residuals from the regression models fitted to the Post-harvested dataset: (a–c): ${\mathcal{M}}_3$-TLW; (d–f): ${\mathcal{M}}_3$-Weibull.