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Record Values Theory and Applications : Record Values S - Mohammad Ahsanullah

Record Values Theory and Applications

Record Values S

Hardcover Published: 28th April 2004
ISBN: 9780761827948
Number Of Pages: 322

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In this book, Mohammad Ahsanullah provides a detailed description of the general theory and applications of record values. Professor Ahsanullah thoroughly discusses the most useful distributions and inferences based on record values, resulting in conclusions that are not available in previously published works. The book, written on an intermediate level that requires the basic knowledge of calculus, probability theory, and mathematical statistics, can be used as a text for advanced undergraduate or graduate level courses.

Prefacep. vii
Abbreviationsp. viii
Record Statistics
Introduction and Examples of Record Valuesp. 1
Definition of Record Values and Record Timesp. 2
The Exact Distribution of Record Valuesp. 2
Moments of Record Valuesp. 8
Distribution of Inter-Record Timesp. 25
Relation Between Occurrences of Records and Poisson Processesp. 37
Number of Records In A Sequence of Observationsp. 39
Distribution of Inter-Record Timesp. 42
The K-Recordsp. 43
Entropies of Record Valuesp. 60
Exponential Distribution
Introductionp. 63
Distribution of Record Valuesp. 64
Moments of Record Valuesp. 66
Estimation of Parametersp. 74
Characterizationsp. 78
Prediction of Record valuesp. 96
Limiting Distributions of Record Valuesp. 98
Generalized Extreme Value Distribution
Introductionp. 101
Distributional Propertiesp. 104
Recurrence Relations Between Momentsp. 106
Estimation of Parametersp. 112
Prediction of Record Valuesp. 122
Characterizationsp. 123
Applicationsp. 125
Limiting Distributionsp. 129
Generalized Pareto Distribution
Introductionp. 131
Distributional Propertiesp. 132
Recurrence Relations of Momentsp. 134
Estimation of Parametersp. 142
Prediction of Record Valuesp. 146
Classical Pareto Distributionp. 137
Lomax Distributionp. 150
Power Function Distribution
Introductionp. 155
Distributional Propertiesp. 156
Recurrence Relations Between Momentsp. 158
Estimation of Parametersp. 165
Prediction of Record Valuesp. 169
One Parameter Uniform Distributionp. 171
Discrete Distribution
Introductionp. 177
Geometric Distributionp. 181
Records of Non-Identically Distributed Random Variablesp. 192
Weak Recordsp. 195
Some Selected Distributions
Introductionp. 209
Logistic Distributionp. 209
Normal Distributionp. 215
Rayleigh Distributionp. 218
Two Parameter Uniform Distributionp. 224
Weibull Distributionp. 233
Distributions Where Consecutive Record Values Have Linear Regressionp. 240
Additional Topics
Introductionp. 249
Limiting Distribution of Inter-Record timesp. 249
Limiting Distribution of Record Valuesp. 252
Limiting Distribution of Record Timesp. 254
Representation of Recordsp. 256
Limiting Distribution of Number of Recordsp. 258
Random Record Modelp. 261
Records of Dependent Sequencep. 267
Concomitantsp. 269
Stirling Numbers of the First Kindp. 275
Bernoulli Numbersp. 276
Cauchy Type Functional Equationp. 277
Complements and Problemsp. 281
Referencesp. 293
Indexp. 315
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9780761827948
ISBN-10: 0761827943
Series: Record Values S
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 322
Published: 28th April 2004
Publisher: University Press of America
Country of Publication: US
Dimensions (cm): 22.1 x 16.5  x 2.7
Weight (kg): 0.64