Ebook: Fuzzy Probability and Statistics

This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.

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This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.

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This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-6
Fuzzy Sets....Pages 7-19
Fuzzy Probability Theory....Pages 21-49
Discrete Fuzzy Random Variables....Pages 51-60
Continuous Fuzzy Random Variables....Pages 61-74
Estimate ?, Variance Known....Pages 75-79
Estimate ?, Variance Unknown....Pages 81-83
Estimate p, Binomial Population....Pages 85-87
Fuzzy Arrival/Service Rates....Pages 89-94
Fuzzy Uniform....Pages 95-99
Fuzzy Max Entropy Principle....Pages 101-105
Max Entropy: Crisp Discrete Solutions....Pages 107-114
Max Entropy: Crisp Continuous Solutions....Pages 115-124
Tests on ?, Variance Known....Pages 125-141
Tests on ?, Variance Unknown....Pages 143-149
Tests on p for a Binomial Population....Pages 151-157
Fuzzy Correlation....Pages 159-162
Estimation in Simple Linear Regression....Pages 163-166
Fuzzy Prediction in Linear Regression....Pages 167-170
Hypothesis Testing in Regression....Pages 171-175
Estimation in Multiple Regression....Pages 177-179
Fuzzy Prediction in Regression....Pages 181-185
Hypothesis Testing in Regression....Pages 187-192
Fuzzy One-Way ANOVA....Pages 193-195
Fuzzy Two-Way ANOVA....Pages 197-201
Fuzzy Estimator for the Median....Pages 203-207
Random Fuzzy Numbers....Pages 209-217
Selected Maple/Solver Commands....Pages 219-221
Summary and Future Research....Pages 223-234
Back Matter....Pages 235-251
....Pages 253-256