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Common Families of Distribution: Discrete and Continuous with Location and Scale Parameters

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  1. Lecture 5 b Fatenalamri

  2. Common families of distribution • Discrete distribution • 1.discrete uniform distribution • 2.hypergeometric distribution • 3.binomial distribution • 4.poisson distribution • 5.negative binomial distribution

  3. Continues distribution • 1.uniform distribution • 2.gamma distribution • 3.normal distribution • Exponential families • Binomial exponential family • Normal exponential family

  4. Location and scale families • There are three types of families are called • Location families, scale families and location scale families • Theorem 3.5.1 • Let f(x) be any pdf and let and Be any given constants then the function is a pdf

  5. Definition 3.5.2 • Let f(x) be any pdf then the family of pdf f(s- ) • Indexed by the parameter Is called the location family with standard pdf f(x) and is called the location parameter for the family Exponential location family

  6. Definition 3.5.4 • Let f(x) be any pdf. Then for any The family of pdf , indexed by the parameter ,is called the scale family with standard pdf f(x) and is called the scale parameter of family

  7. Definition 3.5.5 • Let f(x) be any pdf. Then for any And any ,the family of pdfs , indexed by parameter is called a location-scale family with standard pdf f(x); is called a location parameter and is called a scale parameter

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