## A Primer on Statistical DistributionsDesigned as an introduction to statistical distribution theory. * Includes a first chapter on basic notations and definitions that are essential to working with distributions. * Remaining chapters are divided into three parts: Discrete Distributions, Continuous Distributions, and Multivariate Distributions. * Exercises are incorporated throughout the text in order to enhance understanding of materials just taught. |

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### Contents

1 | |

I DISCRETE DISTRIBUTIONS | 27 |

II CONTINUOUS DISTRIBUTIONS | 105 |

III MULTIVARIATE DISTRIBUTIONS | 247 |

APPENDIX PIONEERS IN DISTRIBUTION THEORY | 277 |

BIBLIOGRAPHY | 289 |

AUTHOR INDEX | 295 |

297 | |

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### Common terms and phrases

arcsine distribution Bernoulli beta distribution beta(p bivariate bution Cauchy distribution cdf’s central moments characteristic function chi-square coefﬁcient conditional distribution Convolutions corresponding Decompositions deﬁned Deﬁnition degenerate distribution degrees of freedom denote derive Dirichlet distribution distri distributed random variables distribution function distribution with pdf entropy Exercise exponential distribution expression extreme value distribution Factorial moments ﬁnite ﬁrst ﬁxed gamma distribution given Hence hypergeometric independent random variables inﬁnitely divisible integer Intentionally Left Blank joint density function kurtosis Laplace distribution Let X1 limiting distribution linear transformation logistic distribution matrix Moments about zero multinomial multivariate Notations Note order statistics Pearson Poisson distribution probability density function random variables X1 random vector readily obtain respectively sequence Shape Characteristics simply standard exponential standard uniform symmetric takes on values X I X1 X1 and X2