## Probability Distributions Used in Reliability EngineeringThe book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering. |

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### Contents

PREFACE | 1 |

COMMON LIFE DISTRIBUTIONS | 40 |

UNIVARIATE CONTINUOUS DISTRIBUTIONS | 85 |

UNIVARIATE DISCRETE DISTRIBUTIONS | 151 |

BIVARIATE AND MULTIVARIATE DISTRIBUTIONS | 173 |

201 | |

### Common terms and phrases

̂̂ ̂ ̂ ̂ 2nd Central 4th Central approximation asymptote Balakrishnan Bayesian Non-informative Priors Berger Beta Distribution Binomial distribution calculate Characteristic Function Closed Form component has survived confidence intervals Conjugate Priors Cumulative Density Function Description Parameters Dist of UOI Distribution Formulas PDF Distribution Let distribution parameters Distribution Probability Density Estimation Maximum Likelihood Excess kurtosis exponential distribution failure rate Fisher Information Matrix gamma distribution hazard rate improper prior integer Jeffrey‟s Prior Jiang Kotz Likelihood Function Likelihood Function Likelihood Maximum Likelihood Function Mean 1st Raw Mean Residual Meeker & Escobar MLE estimates MLE Point Estimates Mode Moments Median multivariate Murthy Non-informative Priors Parameter Estimation Maximum Parameters & Description Percentile Function Point Estimates Poisson distribution Prior Posterior Uniform Prior with limits Probability Density Function probability distribution Properties and Moments Reference Prior reliability engineering Resources Online Rinne Scale Parameter shape Type Prior Posterior uniform distribution UOI Likelihood Model UOI Prior Weibull Distribution