We propose and investigate a mixture model of exponential, Lomax and Weibull distributions (ELWD). Besides implementation of maximum likelihood and Bayesian methods to estimate the parameters of this model under complete samples for different sample sizes, an approximation form due to Lindely is used to obtain Bayesian estimates under the squared error loss function. Further, numerical illustration through Monte Carlo simulation had been provided.

mixture model, maximum likelihood method, Bayesian method, Lindely approximation.