Data Deep Dive

Let \(X_{1},X_{2},X_{3},...............X_{n}\) be an identically independent sample drawn from the exponential family. `f(x …

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…

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-…

Example 4.3: Let \( X_1, X_2, \dots, X_n \) be a random sample from the Poisson distribution \( P(\theta) \) with parameter \( \thet…

Information Inequality In this chapter, the lower bounds $B(\theta)$ for the variance, which is the smallest variance that can be attained…

Let  $x_1, x_2, x_3,...........,x_n$ denote the observations taken from a $Uniform \\ Distribution$ with pdf: `f(x, \theta) =   1 ; \theta …

If we consider a sequence of independent $Bernoulli  \,  Trials$ each trials has two outcomes called "success" or "failure".…

Let $r$ be the number of success resulting from $n$ independent trials with unknown success probability $p$, such that $X$ follows $Binomial$ …

The data collected on the behaviour of the parameter $\theta$ in the form of a sample $X_{1},X_{2},X_{3},...........,X_{n}$.  it is not cos…

The pdf of exponential distribution is given as  `f(x; \theta) = \frac{1}{\theta} e^{-x / \theta}, \quad x \geq 0, \, \theta > 0.` Th…

The probability density function of poisson distribution is given by `P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}, \quad x = 0, 1, 2, \ldots, \, \l…