Consider a set of observed data samples \( X={X_1,X_2,X_3,\cdots X_N} \) and \( \theta \) is the scalar parameter that is to be estimated from the observed samples. The accuracy…

# Tag: MLE

The criteria for existence of having an Minimum Variance Unbiased Estimator (MVUE) was discussed in a previous article. To have an MVUE, it is necessary to have estimates that are…

As we have seen in the previous articles, that the estimation of a parameter from a set of data samples depends strongly on the underlying PDF. The accuracy of the estimation…

As a pre-requisite, check out the previous article on the logic behind deriving the maximum likelihood estimator for a given PDF. Let X=(x1,x2,…, xN) are the samples taken from Gaussian…

As a pre-requisite, check out the previous article on the logic behind deriving the maximum likelihood estimator for a given PDF. Let X=(x1,x2,…, xN) are the samples taken from Exponential…

Suppose X=(x1,x2,…, xN) are the samples taken from a random distribution whose PDF is parameterized by the parameter \(\theta \). If the PDF of the underlying parameter satisfies some regularity…

Likelihood Function: Suppose \(X=(x_1,x_2,\cdots, x_N)\) are the samples taken from a random distribution whose PDF is parameterized by the parameter \(\theta\). The likelihood function is given by \begin{align*}L(\theta;X) &= \prod_{i=1}^{N}…

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