Abstract
<em>The main purpose of this work is to explore the income distribution of both male and female in Pakistan over the period of 2010-2011. For this purpose, the lognormal distribution with known parameters is used as a model and its unknown parameters are estimated by three methods that are likelihood, moments and L-moments. The results show that citizens of Pakistan are not equal in income and the probability plot suggested that the income of the male is greater than that of a female in Pakistan. Moreover, for small sample size, the best method of parameters estimation is the L-moments, while, for large sample size the best method is a maximum likelihood. Findings of the study suggest that suitable policy is required to maintain equality in income distribution in the country. It will consequently reduce the gap among rich and poor and will certainly improve social welfare.</em>
Highlights
The importance of income throughout the world is undeniable
Unluckily the ratio of poverty becomes an increase in the 1990s and the economist focuses to find the ratio of the poor population instead of improving the measurement of the income distribution
In last we compare the parameters of lognormal distribution obtained by L-moments method, Moments method, and Maximum likelihood method, with respect to absolute Bias and RMSE
Summary
The importance of income throughout the world is undeniable. It is a backbone for a country, especially in Pakistan is important as breathing air, without air there is no hope for life. The lognormal distribution (Note 1) is used in several fields of life for estimation of parameters, e.g., they are used in Statistics, Geology, Medical Science, Environmental Science, Technology, Ecology, Social science, and income. Incomes within countries generally adopt a skewed distribution with a long heavy tail. Lognormal distribution has been found best fit on the average for income distribution. This can prove through the goodness of fit test such as Chi-square test, Anderson Darling test (Albreht & Klazinga, 2009)
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