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

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.

Automated summary

This work introduces an extension of the Lindley-Weibull distribution, which is obtained by using the quotient of two independent random variables. The new distribution's pdf, cdf, and risk functions are presented and its statistical properties, moments, skewness, and kurtosis are studied. The parameter estimation is done using the maximum likelihood method and assessed through a Monte Carlo simulation study, with nutrition data used as an example to illustrate the proposed model's utility.