The Properties and Parameter Estimation of Left-Truncated Skew-Normal Distribution

Meilin Han

doi:10.6919/ICJE.202412_10(12).0016

Authors

Meilin Han

DOI:

https://doi.org/10.6919/ICJE.202412_10(12).0016

Keywords:

Nonnegative Data; Skew Normal Distribution; Location-Scale Extended Family; Maximum Likelihood Estimation.

Abstract

Regarding the double truncated skew normal distribution proposed by Flecher et al. (2010), we explore a special case when its upper bound tends to infinity -- the left-truncated skew-normal distribution. Specifically, this paper investigates its relevant properties, such as the expressions of the density function, cumulative distribution function, moments, and moment generating function. Additionally, we obtain the expression form of the location-scale extended family of the zero-truncated skew-normal distribution and employ the maximum likelihood method to estimate the parameters of the location-scale extended family distribution. Finally, the performance of the maximum likelihood estimation is evaluated using Monte Carlo simulation.

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