Literature in Testing of Hypotheses: Concepts, Theory, and Applications
Testing of Hypothesis In statistical hypothesis testing, our goal is to use sample data to make decisions about population character…
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Power Series Distribution and it's applications
Power Series Distribution Power series distributions are the discrete type of distributions and we can say it they are family of some other distr…
Analysis of Variance - Statsclick
Introduction Suppose that we wish to be more objective in our analysis of the data. Specifically, suppose that we wish to test for differences …
Regular Exponential Family of Distributions
Let \(X_{1},X_{2},X_{3},...............X_{n}\) be an identically independent sample drawn from the exponential family. `f(x …
Cramer Rao lower bound in Bernoulli Distribution
Finding the UMVUE and CR Bound Let $X_1, X_2, X_3, \dots, X_n$ be a random sample drawn from a Bernoulli distribution $B(1, \theta)$. We aim to fin…
Cramer Rao lower bound in uniform distribution - statsclick
Lower bound and UMVUE estimation Let $X_1, X_2, \dots, X_n$ be a random sample from $U(0, \theta)$. We examine the application of the Cramér-…
Estimation of Lower Bound in Poisson Distribution
Example 4.3: Let \( X_1, X_2, \dots, X_n \) be a random sample from the Poisson distribution \( P(\theta) \) with parameter \( \thet…
Cramer Rao Inequality - statsclick
Information Inequality In this chapter, the lower bounds $B(\theta)$ for the variance, which is the smallest variance that can be attained…