European Journal of Statistics and Probability (EJSP)

# Moment Generating Function

## The Iwok-Nwikpe Distribution: Statistical Properties and Application (Published)

In this paper, a new continuous probability distribution named ‘Iwok-Nwikpe distribution’ is proposed. Some of the important statistical properties of the new distribution were derived. The shapes of the probability density function, cumulative distribution function and the survival function have been displayed for different values of the parameter.  The moment generating function, the first three raw moments, the second and third moments about the mean and the distribution of order statistics were also derived. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Iwok-Nwikpe distribution was demonstrated using some real life data sets. The goodness of fit showed that the Iwok-Nwikpe distribution outperforms the one parameter exponential, Lindley, Shanker, Sujatha and Amarendra distributions for the data sets used in this work

## A Three – Parameter Sujatha distribution with Application (Published)

In this paper, a new three-parameter continuous probability distribution is proposed. The new distribution is a modification of ‘’A two-parameter generalization of Sujatha distribution (AGSD)’’ proposed by Shanker et al (2017). Some important statistical properties of the new distribution were derived. The shape of its probability density function is given for selected values of the parameters.  The mathematical expression for the moment generating function, the first four raw moments and the distribution of order statistics has been established. The parameters of the new distribution were estimated using maximum likelihood method. The graph of the hazard function reveals that the distribution has an increasing hazard rate. The flexibility of the new distribution was demonstrated using a real life data set. The goodness of fit showed that the three-parameter distribution gave a better fit than the exponential, Akash, Shanker and Amarendra distributions for the data set used.

## On The Modified Extended Generalized Exponential Distribution (Published)

A modification on the extension of generalized exponential distribution due to Olapade (2014) is presented in this paper and some of its properties, such as; The cumulative distribution function, the survival function, the hazard function and it properties, the reverse hazard function, the moment generating function, the  moment about the origin, the median, the percentile point and the associated initial-value problem (IVP) for ordinary differential equation (O.D.E.) are established.

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