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December 2024

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 \…
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