Advanced Mathematical Models & Applications

Length biased distributions are special cases of weighted distributions. We used this idea in this paper to propose a generalization of a one-parameter linear exponential distribution. The various characteristics of the recommended distribution are deduced and explored in detail. Some numerical studies are implemented; they demonstrate that the distribution is skewed to the right with a heavier tail than the normal distribution. The mean waiting time and residual life time are also studied. To estimate the distribution's parameters, six methods of estimation are employed. A simulation study is conducted, which shows that the estimators are approximately unbiased and consistent. Three real financial data sets are applied. They represent earning per share in the financial, industry and service sectors at the Amman Stock Exchange. They show that the suggested distribution has the best fit for these data sets compared to some competence distributions.