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. 2021 Sep 14;49(16):4206-4224.
doi: 10.1080/02664763.2021.1975661. eCollection 2022.

The modified slash Lindley-Weibull distribution with applications to nutrition data

Jimmy Reyes  1 , Jaime Arrué  1 , Osvaldo Venegas  2 , Héctor W Gómez  1
Affiliations

The modified slash Lindley-Weibull distribution with applications to nutrition data

Jimmy Reyes et al. J Appl Stat. .

Abstract

This work presents an extension of the slash Lindley-Weibull distribution, of which it can be considered a modification. The new family is obtained by using the quotient of two independent random variables: a two-parameter Lindley-Weibull distribution divided by a power of the exponential distribution with parameter equal to 2. We present the pdf and cdf of the new distribution, analyzing their risk functions. Some statistical properties are studied and the moments and coefficients of asymmetry and kurtosis are shown. The parameter estimation problem is carried out by the maximum likelihood method. The method is assessed by a Monte Carlo simulation study. We use nutrition data, which are characterized by high kurtosis, to illustrate the usefulness of the proposed model.

Keywords: Slash Lindley–Weibull distribution; maximum likelihood; moments; regression.

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Conflict of interest statement

No potential conflict of interest was reported by the authors.

Figures

Figure 1.
Figure 1.
Pdf of the MSLW(β,α) distribution for different values of α and β.
Figure 2.
Figure 2.
Cdf of the MSLW distribution for different values of α and β.
Figure 3.
Figure 3.
The hazard rate functions for the MSLW distribution for different values of α and β.
Figure 4.
Figure 4.
Asymmetry coefficient (left panel)and kurtosis coefficient (right panel) of the MSLW distribution.
Figure 5.
Figure 5.
Betaplasma: Histogram and fitted pdfs of the MSLW, SLW and LW distributions.
Figure 6.
Figure 6.
Betaplasma: Q-Q plots for the MSLW (a), SLW (c) and LW (c) distributions.
Figure 7.
Figure 7.
Betaplasma: KS plots for the MSLW, SLW and LW distributions.
Figure 8.
Figure 8.
TTT-plot for the Betaplasma data set.
See this image and copyright information in PMC

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