%0 Journal Article
%T Statistical Inferences and Applications of the Half Exponential Power Distribution
%A Wenhao Gui
%J Journal of Quality and Reliability Engineering
%D 2013
%R 10.1155/2013/219473
%X We investigate the statistical inferences and applications of the half exponential power distribution for the first time. The proposed model defined on the nonnegative reals extends the half normal distribution and is more flexible. The characterizations and properties involving moments and some measures based on moments of this distribution are derived. The inference aspects using methods of moment and maximum likelihood are presented. We also study the performance of the estimators using the Monte Carlo simulation. Finally, we illustrate it with two real applications. 1. Introduction The well-known exponential power (EP) distribution or the generalized normal distribution has the following density function: where is the shape parameter. This family consists of a wide range of symmetric distributions and allows continuous variation from normality to nonnormality. It includes the normal distribution as the special case when and the Laplace distribution when . Nadarajah [1] provided a comprehensive treatment of its mathematical properties. Its tails can be more platykurtic ( ) or more leptokurtic ( ) than the normal distribution ( ). The distribution has been widely used in the Bayes analysis and robustness studies (see Box and Tiao [2], Genc [3], Goodman and Kotz [4], and Tiao and Lund [5].) On the other hand, since the most popular models used to describe the lifetime process are defined on nonnegative measurements, which motivate us to take a positive truncation in the model (1) and develop a half exponential power (HEP) distribution. As far as we know, this model has not been previously studied although, we believe, it plays an important role in data analysis. The resulting nonnegative half exponential power distribution generalizes the half normal (HN) distribution, and it is more flexible. In our work, we aim to investigate the statistical features of the nonnegative model and apply them to fit the lifetime data. The rest of this paper is organized as follows: in Section 2, we present the new distribution and study its properties. Section 3 discusses the inference, moments, and maximum likelihood estimation for the parameters. In Section 4, we discuss a useful technique, a half normal plot with a simulated envelope, to assess the model adequacy. Simulation studies are performed in Section 5. Section 6 gives two illustrative examples and reports the results. Section 7 concludes our work. 2. The Half Exponential Power Distribution 2.1. The Density and Hazard Function Definition 1. A random variable has a half exponential power slash distribution if
%U http://www.hindawi.com/journals/jqre/2013/219473/