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Characterizations of Univariate Continuous Distributions

:	Mohammad Ahsanullah
:	Characterizations of Univariate Continuous Distributions
:	Atlantis Press
:	9789462391390
:	1
:	CHF 85.40
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	130
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos& Kotz 'Characterizations of Probability Distributions' (Springer), together with applications of the theory in model fitting and predictions.

	Preface	7
	Contents	8
	1 Introduction	10
	1.1 Distribution of Univariate Continuous Distribution	10
	1.2 Moment Generating and Characteristic Functions	10
	1.3 Some Reliability Properties	11
	1.4 Cauchy Functional Equations	12
	1.5 Order Statistics	13
	1.6 Record Values	14
	1.7 Generalized Order Statistics	19
	1.8 Lower Generalized Order Statistics (Lgos)	21
	1.9 Some Useful Functions	24
	2 Some Continuous Distributions	25
	2.1 Beta Distribution	25
	2.2 Cauchy Distribution	26
	2.3 Chi-Squared Distribution	27
	2.4 Exponential Distribution	28
	2.5 F-Distribution	30
	2.6 Gamma Distribution	31
	2.7 Gumbel Distribution	32
	2.8 Inverse Gaussian (Wald) Distribution	33
	2.9 Laplace Distribution	34
	2.10 Logistic Distribution	35
	2.11 Lognormal Distribution	36
	2.12 Normal Distribution	37
	2.13 Pareto Distribution	38
	2.14 Power Function Distribution	39
	2.15 Rayleigh Distribution	40
	2.16 Student’s t-Distribution	41
	2.17 Weibull Distribution	41
	3 Characterizations of Distributions by Independent Copies	43
	3.1 Characterization of Normal Distribution	43
	3.2 Characterization of Levy Distribution	52
	3.3 Characterization of Wald Distribution	53
	3.4 Characterization of Exponential Distribution	54
	3.5 Characterization of Symmetric Distribution	56
	3.6 Charactetrization of Logistic Disribution	57
	3.7 Characterization of Distributions by Truncated Statistics	57
	3.7.1 Characterization of Semi Circular Distribution	59
	3.7.2 Characterization of Lindley Distribution	59
	3.7.3 Characterization of Rayleigh Distribution	61
	4 Characterizations of Univariate Distributions by Order Statistics	62
	4.1 Characterizations of Student’s t Distribution	62
	4.2 Characterizations of Distributions by Conditional Expectations (Finite Sample)	66
	4.3 Characterizations of Distributions by Conditional Expectations (Extended Sample)	68
	4.4 Characterizations Using Spacings	69
	4.5 Characterizations of Symmetric Distribution Using Order Statistics	72
	4.6 Characterization of Exponential Distribution Using Conditional Expectation of Mean	73
	4.7 Characterizations of Power Function Distribution by Ratios of Order Statistics	74
	4.8 Characterization of Uniform Distribution Using Range	76
	4.9 Characterization by Truncated Order Statistics	78
	5 Characterizations of Distributions by Record Values	79
	5.1 Characterizations Using Conditional Expectations	79
	5.2 Characterization by Independence Property	82
	5.3 Characterizations Based on Identical Distribution	88
	6 Characterizations of Distributions by Generalized Order Statistics	95
	6.1 Characterizations by Conditional Expectations	95
	6.2 Characterizations by Equality of Expectations of Normalized Spacings	101
	6.3 Characterizations by Equality of Distributions	101
	References	104
	Index	130