The non – central t – distribution is the distribution of the ratio of a normal variate with possibly non – zero mean and variate unity, to the square root of an independent χ2 – variate divided by its degrees of freedom. If X ≈ N(μ, 1) and Y is an independent χ2 – variate with n degrees of freedom then

Is said to have a non – central t – distribution with n degrees of freedom and non – centrality parameter μ. Non – central t – distribution is required for the power functions of certain tests concerning normal population.

Probability density function of ‘t’. since X ≈ N(μ, 1)

Which is the probability density function of non – central t – distribution with n degrees of freedom and non – centrality element µ.

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