Application of Hyperbolic Secant Distributions

• Sibuya Masaaki

  Department of Business Administration, Takachiho University

Bibliographic Information

Other Title

• 双曲線正割分布の応用
• ソウキョクセン セイカツ ブンプ ノ オウヨウ

Abstract

The hyperbolic secant distribution (HpSc) is one of six subfamilies of the natural exponential family with quadratic variance functions, NEF-QVF. The others are normal, gamma, Poisson, binomial and negative binomial distributions. It is, however, little-known and rarely used in applied statistics. In this paper, its properties are surveyed and graphically visualized; new facts on the moments, mode, and conjugate prior distribution are shown; ML estimation, generalized linear model and generalized additive model are explored. HpSc models are fitted to some data sets, and the results are preferable to the conventional ones. Some numerical procedures are to be developed, and further research will be promising.

Journal

• Ouyou toukeigaku

  Ouyou toukeigaku 35 (1), 17-47, 2006

  Japanese Society of Applied Statistics

Keywords

• dispersion model
• gamma and digamma functions of complex variable
• GHS distributions
• glim interface
• hyperbolic cosine distribution
• Morris'class
• Morris't distribution
• unimodality

Details

• CRID: 1390001204441755392
• NII Article ID: 10018231118
• NII Book ID: AN00330942
• DOI: 10.5023/jappstat.35.17
• ISSN: 18838081
• ISSN: 02850370
• NDL BIB ID: 8054729
• Web Site: http://id.ndl.go.jp/bib/8054729
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I8054729
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed