No abstract

The Bayesian estimation of unknown parameter of the Poisson distribution is examined under different priors. The posterior distributions for the unknown parameter of the Poisson distribution are derived using the following priors: uniform, Jeffrey's, Gamma distribution, Gamma-Chi-square distribution, Gammaexponential distribution and Chi-square-exponential distribution. Numerical and graphical illustrations of the posterior densities of the parameters of interest were conducted using R Software.

Lognormal distribution is widely used in scientific field, such as agricultural, entomological, biology etc. If a variable can be thought as the multiplicative product of some positive independent random variables, then it could be modelled as lognormal. In this study, maximum likelihood estimates and posterior estimates of the parameters of lognormal distribution are obtained and using these estimates we calculate the point estimates of mean and variance for making comparisons.

Prime Minister Imran Khan introduced an interest-free loan programme through a public-private collaboration as part of the Kamyab Jawan Programme 2022. A huge number of low-income and susceptible households benefited immensely from this programme. This program's goal is to end poverty by giving low-income individuals interest-free loans to launch their own small businesses. Primary data for this research was gathered from 184 beneficiaries of the lenders who received interest-free loans from the prime minister under the Kamyab Jawan programme in two districts of Sindh. Records of beneficiaries were taken from two chosen districts, and each component was chosen using a simple random sampling method. For this study, study participants of both genders were represented equally. A self-managed device was used to gather data directly from the recipients of the Prime Minister's interest-free loans. The findings show that the Prime Minister's Interest Free Loan Program is significantly enhancing the socioeconomic, economic, and social and political wellness of the recipients. Most survey participants reported significantly improved financial, personal, and sociopolitical wellness. Enhanced social, financial, and political wellness were also found to be related to interest-free loans in one sample binominal assessment. The majority of participants expressed satisfaction with the interest-free loan programme offered by the Kamyab Jawan programme, believing that it had a significant impact on decreasing the level of security vulnerabilities and poverty following the COVID-19 disease outbreak. The study's author suggested that this program's based on geography reach be increased in some way to attain as many poor and vulnerable communities as possible.