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

This lecture explores common families of distributions, including discrete distribution, continuous distribution, exponential families, and location and scale families. It covers key concepts and definitions related to these families and their parameters.

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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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