Handbook of statistical distributions with applications

Table of Contents STATCALC Introduction Contents of StatCalc PRELIMINARIES Random Variables and Expectations Moments and Other Functions Some Functions Relevant to Reliability Model Fitting Methods of Estimation Inference Pivotal-Based Methods for Location-Scale Families Method of Variance Estimate Recovery Modified Normal-Based Approximation Random Number Generation Some Special Functions DISCRETE UNIFORM DISTRIBUTION Description Moments BINOMIAL DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Proportion Prediction Intervals Tolerance Intervals Tests for the Difference between Two Proportions Two-Sample Confidence Intervals for Proportions Confidence Intervals for a Linear Combination of Proportions Properties and Results Random Number Generation Computation of Probabilities HYPERGEOMETRIC DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Point Estimation Test for the Proportion and Power Calculation Confidence Interval and Sample Size Calculation A Test for Comparing Two Proportions Properties and Results Random Number Generation Computation of Probabilities POISSON DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Model Fitting with Examples One-Sample Inference Test for the Mean Confidence Intervals for the Mean Prediction Intervals Tolerance Intervals Tests for Comparing Two Means and Power Calculation Confidence Intervals for the Ratio of Two Means Confidence Intervals for the Difference between Two Means Inference for a Weighted Sum of Poisson Means Properties and Results Random Number Generation Computation of Probabilities GEOMETRIC DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Properties and Results Random Number Generation NEGATIVE BINOMIAL DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Point Estimation A Test for the Proportion Confidence Intervals for the Proportion Properties and Results Random Number Generation A Computational Method for Probabilities LOGARITHMIC SERIES DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Inferences Properties and Results Random Number Generation A Computational Algorithm for Probabilities CONTINUOUS UNIFORM DISTRIBUTION Description Moments Inferences Properties and Results Random Number Generation NORMAL DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments One-Sample Inference Two-Sample Inference Tolerance Intervals Properties and Results Relation to Other Distributions Random Number Generation Computing the Distribution Function CHI-SQUARE DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Applications Properties and Results Random Number Generation Computing the Distribution Function F DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Properties and Results Random Number Generation A Computational Method for Probabilities STUDENT'S t DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Distribution of the Maximum of Several |t| Variables Properties and Results Random Number Generation Computation of the Distribution Function EXPONENTIAL DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Inferences Properties and Results Random Number Generation GAMMA DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Applications with Some Examples Inferences Properties and Results Random Number Generation A Computational Method for Probabilities BETA DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Inferences Applications with an Example Properties and Results Random Number Generation Evaluating the Distribution Function NONCENTRAL CHI-SQUARE DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Applications Properties and Results Random Number Generation Evaluating the Distribution Function NONCENTRAL F DISTRIBUTION Description Moments Computing Table Values Applications Properties and Results Random Number Generation Evaluating the Distribution Function NONCENTRAL t DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Applications Properties and Results Random Number Generation Evaluating the Distribution Function LAPLACE DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Inferences Applications Relation to Other Distributions Random Number Generation LOGISTIC DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Maximum Likelihood Estimators Applications Properties and Results Random Number Generation LOGNORMAL DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Maximum Likelihood Estimators Confidence Interval and Test for the Mean Inferences for the Difference between Two Means Inferences for the Ratio of Two Means Applications Properties and Results Random Number Generation Calculation of Probabilities and Percentiles PARETO DISTRIBUTION Description Moments Computing Table Values Inferences Applications Properties and Results Random Number Generation Computation of Probabilities and Percentiles WEIBULL DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Applications Point Estimation Properties and Results Random Number Generation EXTREME VALUE DISTRIBUTION Description Moments Computing Table Values Maximum Likelihood Estimators Applications Properties and Results Random Number Generation CAUCHY DISTRIBUTION Description Moments Computing Table Values Inference Applications Properties and Results INVERSE GAUSSIAN DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments One-Sample Inference Two-Sample Inference Random Number Generation RAYLEIGH DISTRIBUTION Description Moments Probabilities, Percentiles, and Moments Maximum Likelihood Estimator Relation to Other Distributions Random Number Generation BIVARIATE NORMAL DISTRIBUTION Description Computing Probabilities Inferences on Correlation Coefficients Inferences on the Difference between Two Correlation Coefficients Test and Confidence Interval for Variances Some Properties Random Number Generation A Computational Algorithm for Probabilities SOME NONPARAMETRIC METHODS Distribution of Runs Sign Test and Confidence Interval for the Median Wilcoxon Signed-Rank Test and Mann-Whitney U Statistic Wilcoxon Rank-Sum Test Quantile Estimation and Nonparametric Tolerance Interval

Easy-to-Use Reference and Software for Statistical Modeling and Testing Handbook of Statistical Distributions with Applications, Second Edition provides quick access to common and specialized probability distributions for modeling practical problems and performing statistical calculations. Along with many new examples and results, this edition includes both the author's StatCalc software and R codes to accurately and easily carry out computations. New to the Second Edition Major changes in binomial, Poisson, normal, gamma, Weibull, exponential, logistic, Laplace, and Pareto distributions Updated statistical tests and intervals based on recent publications in statistical journals Enhanced PC calculator StatCalc with electronic help manuals R functions for cases where StatCalc is not applicable, with the codes available online This highly praised handbook integrates popular probability distribution models, formulas, applications, and software to help you compute a variety of statistical intervals. It covers probability and percentiles, algorithms for random number generation, hypothesis tests, confidence intervals, tolerance intervals, prediction intervals, sample size determination, and much more.