1. Lecture 5 b
Faten alamri

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