Tilted Normal Distribution and Its Survival Properties

Abstract

To analyze skewed data, skew normal distribution is proposed by Azzalini (1985). For practical problems of estimating the skewness parameter of this distribution, Gupta and Gupta ( 2008) suggested power normal distribution as an alternative. We search for another alternative, named tilted normal distribution following the approach of Marshall and Olkin (1997) to add a positive parameter to a general survival function and taking survival function is of normal form. We have found out different properties of this distribution. Maximum likelihood estimate of parameters of this distribution have been found out. Comparison of tilted normal distribution with skew normal and power normal distribution have been made.