# On the Shifted Hybrid Log-Normal Distribution

## DOI:

https://doi.org/10.6092/issn.1973-2201/12904## Keywords:

Hybrid log-normal distribution, Estimation, Lifetime data, Fracture toughness data, Simulation## Abstract

The log-normal distribution is widely used to model positive valued data in many areas of applied research. However, sometimes the log-normal distribution does not completely satisfy the fitting expectations in every real life situations. In this paper, we introduce, investigate, and discuss a more flexible shifted hybrid log-normal distribution for which the log-normal distribution is a special case. Also, various properties, special cases and estimation procedure of the new distribution are discussed. Moreover, the performances of maximum likelihood estimators of the parameters are examined using a brief simulation study. The flexibility and performance of the newdistribution is also illustrated through two applications by fitting two real datasets of different situations.

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*Statistica*,

*82*(4), 417–431. https://doi.org/10.6092/issn.1973-2201/12904

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