Problem 43E

Let Y1, Y2, . . . , Yn denote independent and identically distributed random variables from a power family distribution with parameters α and θ. Then, by the result in Exercise 6.17, if α, θ > 0,

Reference

A member of the power family of distributions has a distribution function given by

a Find the density function.

b For fixed values of α and θ, find a transformation G(U ) so that G(U ) has a distribution function of F when U possesses a uniform (0, 1) distribution.

c Given that a random sample of size 5 from a uniform distribution on the interval (0, 1) yielded the values .2700, .6901, .1413, .1523, and .3609, use the transformation derived in part (b) to give values associated with a random variable with a power family distribution with α = 2, θ = 4.

Statistics 130M Notes January 19, 2017 notes= January 26, 2017 class Tuesday January 24, 2017 Sick- Skipped Class. Sorry All Thursday January 26, 2017 Chapter 3 Numerical descriptive techniques - Allows us to be precise - Most mathematical calculations Information - When interrupting a histogram we focus on shape Population - Described by parameters - Parameters are often written using greek letters Summaries for symmetric distribution - Central tendency o Balancing point/ halfway point o ***should be same**** o Average of mean o Center of symmetric distribution Skewed distribution - Extreme values/ outliers effected the average - Curve killer - Don’t use balancing point Arithmetic mean