Penalized Likelihood Parameter Estimation in the Quasi Lindley and Nadarajah-Haghighi Distributions

The issues of performing inference on the parameters of quasi-Lindley (QL) distribution and Nadarajah-Haghighi exponential distribution (N-H) is addressed. It is shown graphically that the likelihood function of the quasi-Lindley distribution and Nadarajah-Haghighi exponential distribution is configured with a flat monotone shape. Which makes it very difficult to pick the values of the parameters that maximize the likelihood function. A penalization scheme is used to improve maximum likelihood point estimation. A penalization scheme based on the Jeffreys prior.