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

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• The slash Lindley-Weibull distribution is a known statistical model.
• Modifications and extensions of existing distributions are crucial for improving statistical analysis capabilities.

Purpose of the Study:

• To introduce a new statistical distribution family as a modification of the slash Lindley-Weibull distribution.
• To analyze the properties and potential applications of this novel distribution.

Main Methods:

• The new distribution is constructed using the quotient of a two-parameter Lindley-Weibull distribution and a power of an exponential distribution.
• Probability density function (pdf) and cumulative distribution function (cdf) are derived.
• Statistical properties, including moments, asymmetry, and kurtosis coefficients, are studied.
• Parameter estimation is performed using the maximum likelihood method.
• A Monte Carlo simulation study assesses the estimation method's performance.

Main Results:

• The probability density function (pdf) and cumulative distribution function (cdf) of the new distribution are presented.
• Analysis of risk functions and key statistical properties (moments, asymmetry, kurtosis) are provided.
• The maximum likelihood estimation method is validated through simulation.
• The proposed model demonstrates utility in analyzing nutrition data, which often exhibits high kurtosis.

Conclusions:

• A new statistical distribution, extending the slash Lindley-Weibull distribution, has been successfully developed.
• The derived distribution and its properties are well-defined.
• The model shows practical applicability, particularly for datasets with high kurtosis, such as nutrition data.