Beta-normal distribution and its applications

被引:822
作者
Eugene, N [1 ]
Lee, C [1 ]
Famoye, F [1 ]
机构
[1] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA
关键词
symmetry; skewness; bimodality; order statistics; moments; estimation;
D O I
10.1081/STA-120003130
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];
摘要
This paper introduces a general class of distributions generated from the logit of the beta random variable. A special case of this family is the beta-normal distribution. The shape properties of the beta-normal distribution are discussed. Estimation of parameters of the beta-normal distribution by the maximum likelihood method is also discussed. The beta-normal distribution provides great flexibility in modeling not only symmetric heavy-tailed distributions, but also skewed and bimodal distributions. The flexibility of this distribution is illustrated by applying it to two empirical data sets and comparing the results to previously used methods.
引用
收藏
页码:497 / 512
页数:16
相关论文
共 19 条
[1]
Amoroso L., 1925, ANN MATH 4, V2, P123
[2]
[Anonymous], 1965, STAT REV
[3]
A GENERAL DISTRIBUTION FOR DESCRIBING SECURITY PRICE RETURNS [J].
BOOKSTABER, RM ;
MCDONALD, JB .
JOURNAL OF BUSINESS, 1987, 60 (03) :401-424
[4]
BOSE RC, 1959, BIOMETRIKA, V46, P433, DOI 10.1093/biomet/46.3-4.433
[5]
GAMMA-DISTRIBUTIONS OF ADULT NUMBERS FOR TRIBOLIUM POPULATIONS IN THE REGION OF THEIR STEADY-STATES [J].
COSTANTINO, RF ;
DESHARNAIS, RA .
JOURNAL OF ANIMAL ECOLOGY, 1981, 50 (03) :667-681
[6]
EUGENE N, 2001, THESIS CENTRAL MICHI
[7]
On the Lagrange gamma distribution [J].
Famoye, F ;
Govindarajulu, Z .
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 1998, 27 (04) :421-431
[8]
[9]
PARAMETER AND QUANTILE ESTIMATION FOR THE GENERALIZED PARETO DISTRIBUTION [J].
HOSKING, JRM ;
WALLIS, JR .
TECHNOMETRICS, 1987, 29 (03) :339-349
[10]
LESLIE PH, 1962, BIOMETRIKA, V49, P1