A Power Maxwell Distribution with Heavy Tails and Applications

Mathematics

Osvaldo Venegas¹  HéctorW. Gómez²  FranciscoA. Segovia³  YolandaM. Gómez³ 

[1] Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile;Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile;Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile;

关键词: Maxwell distribution;    slash distribution;    kurtosis;    maximum likelihood;    EM algorithm;   

DOI  :  10.3390/math8071116

来源: DOAJ

【 摘 要 】

In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data.

【 授权许可】

Unknown