On the Shifted Hybrid Log-Normal Distribution

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.

Keywords

• hybrid log-normal distribution
• estimation
• lifetime data
• fracture toughness data
• simulation