Maximum Likelihood Estimator in Binomial Distribution
Let $r$ be the number of success resulting from $n$ independent trials with unknown success probability $p$, such that $X$ follows $Binomial$ …
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Data Sufficiency and Data Summarization - Theory of Estimation
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…
Maximum Likelihood Estimator in exponential distribution
The pdf of exponential distribution is given as `f(x; \theta) = \frac{1}{\theta} e^{-x / \theta}, \quad x \geq 0, \, \theta > 0.` Th…
Maximum Likelihood Estimator in Poisson Distribution
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…
Maximum Likelihood Estimator for Log Normal Distribution
If $X_{1}, X_{2},......X_{n} ~ LogN(\mu, \sigma^2) \tag{1}$ The pdf of log normal distribution is given by `f(x; \mu, \sigma^2) = \frac…
Maximum likelihood estimation for Normal Distribution
The pdf of Normal distribution is given by: `f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}}` Case 1: MLE for `\mu` when `\si…
Maximum likelihood estimation for Pareto observations
MLE for Pareto distribution The pdf of Pareto distribution is given by: `f(x; \alpha, \lambda) = \frac{\alpha \lambda^\alpha}{x^{\alpha+1}} \quad \…
Methods of Estimation in Statistical Inference
Statistical estimation is the cornerstone of statistical inference, enabling us to derive insights about population characteristics using sample data…