An Extension of the Truncated-Exponential Skew- Normal Distribution

In the paper, we present an extension of the truncated-exponential skew-normal (TESN) distribution. This distribution is defined as the quotient of two independent random variables whose distributions are the TESN distribution and the beta distribution with shape parameters q and 1, respectively. The resulting distribution has a more flexible coefficient of kurtosis. We studied the general probability density function (pdf) of this distribution, its survival and hazard functions, some of its properties, moments and inference by the maximum likelihood method. We carried out a simulation and applied the methodology to a real dataset.

[1]  S. Nadarajah,et al.  Truncated-exponential skew-symmetric distributions , 2014 .

[2]  H. Akaike.  A new look at the statistical model identification , 1974 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  A. B. Simas,et al.  The exp-$G$ family of probability distributions , 2010, 1003.1727.

[5]  Héctor W. Gómez,et al.  A new family of slash-distributions with elliptical contours , 2007 .

[6]  K. Kafadar.  A Biweight Approach to the One-Sample Problem , 1982 .

[7]  D. Stram,et al.  Variance components testing in the longitudinal mixed effects model. , 1994, Biometrics.

[8]  Heleno Bolfarine,et al.  An extension of the generalized Birnbaum-Saunders distribution , 2009 .

[9]  M. Steel,et al.  A Constructive Representation of Univariate Skewed Distributions , 2006 .

[10]  D. F. Andrews,et al.  Stress-Rupture Life of Kevlar 49/Epoxy Spherical Pressure Vessels , 1985 .

[11]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[12]  H. Bolfarine,et al.  A clustering cure rate model with application to a sealant study , 2017 .

[13]  H. Chernoff.  On the Distribution of the Likelihood Ratio , 1954 .

[14]  G. Cordeiro,et al.  The Exponentiated G Poisson Model , 2015 .

[15]  S. Nadarajah,et al.  Poisson Generated Family of Distributions: A Review , 2020, Sankhya B.

[16]  W. Rogers,et al.  Understanding some long-tailed symmetrical distributions , 1972 .

[17]  R. Maller,et al.  Testing for the presence of immune or cured individuals in censored survival data. , 1995, Biometrics.

[18]  M. Genton,et al.  A SKEW-SYMMETRIC REPRESENTATION OF MULTIVARIATE DISTRIBUTIONS , 2002 .