For characterization of negative exponential distribution one needs
any arbitrary non-constant function only in place of approaches such as
identical distributions, absolute continuity, constant regression of order
statistics, continuity and linear regression of order statistics,
non-degeneracy etc. available in the literature. Path breaking different
approach for characterization of negative exponential distribution through
expectation of non-constant function of random variable is obtained. An example
is given for illustrative purpose.
For the characterization of the power function distribution, one needs any arbitrary non constant function only in place of independence of suitable function of order statistics, linear relation of conditional expectation, recurrence relations between expectations of function of order statistics, distributional properties of exponential distribution, record valves, lower record statistics, product of order statistics and Lorenz curve, etc. available in the literature. The goal of this research is not to give a different path-breaking approach for the characterization of power function distribution through the expectation of non constant function of random variable and provide a method to characterize the power function distribution as remark. Examples are given for the illustrative purpose.
Heavy metal contamination of soil resulting from sewage irrigation is a cause of serious concern due to the potential health impacts of consuming contaminated products. In this study an assessment made of the impact of sewage irrigation on heavy metal contamination of Spinach, Cabbage, Beetroot, Reddish, Okra, Tomato, and Cucumber is widely cultivated and consumed in urban India, particularly by the poor. A field study was conducted at seven major sites that were irrigated by either treated, (Dhandupura) or untreated wastewater in the suburban areas of Agra, India. Samples of irrigation water, soil, and the edible portion of all the vegetables were collected monthly during the winter seasons and were analyzed for Fe, Cd, Cu, Zn, and Pb. Heavy metals in irrigation water were below the internationally recom- mended (WHO) maximum permissible limits set for agricultural use for all heavy metals except Cd at all the sites. Similarly, the mean heavy metal concentrations in soil were below the Indian standards for all heavy metals, but the maximum value of Cd recorded during January was higher than the standard. However, in the edible portion of spinach, the Cd concentration was higher than the permissible limits of the Indian standard during summer, whereas Pb concentrations were higher in winter seasons. Results of correlation analysis were computed to assess the relationship between individual heavy metal concentration in the vegetable samples. The study concludes that the use of treated and untreated wastewater for irrigation has increased the contamination of Cd, Pb in edible portion of vegetables causing potential health risk in the long term from this practice. The study also points to the fact that adherence to standards for heavy metal contamination of soil and irrigation water does not ensure safe food. Fe was measured abundant in soil whereas Pb and Cd were found more in untreated sites as compared to treated site. Correlation, paired T-test and ANOVA were also carried out for pre post harvested soil and vegetables.