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Estimation of P(X ≤ Y ) for discrete distributions with non-identical support

100%

Mouli Choudhury M. , Bhattacharya R. , Maiti S. S.

Statistics in Transition new series

2022

tom 23

nr 3

43-64

The Uniformly Minimum Variance Unbiased (UMVU) and the Maximum Likelihood (ML) estimations of R = P(X ≤ Y ) and the associated variance are considered for independent discrete random variables X and Y. Assuming a discrete uniform distribution for X and the distribution of Y as a member of the discrete one parameter exponential family of distributions, theoretical expressions of such quantities are derived. Similar expressions are obtained when X and Y interchange their roles and both variables are from the discrete uniform distribution. A simulation study is carried out to compare the estimators numerically. A real application based on demand-supply system data is provided.

Thermally induced oxidative trimerization of benzimidazole by copper(II) chloride in the solid state

100%

Bhattacharya R. , Ray S. , Ray J. , Ghosh A.

Open Chemistry

2003

tom 1

nr 4

427-440

Benzimidazolium trichlorocuprate(II) undergoes a redox reaction in the solid state at elevated temperature (∼240°C) to produce the cyclic trimer of benzimidazole and cuprous chloride. The trimer has been characterized by IR, NMR, and Mass spectroscopy. It has also been synthesized in lower yield by heating the mixtures of CuCl2 and benzimidazole in different ratios or heating other compounds of CuCl2 and benzimidazole. The absorption, emission, and excitation spectra of the trimer in two different solvents (TFA and DMSO) and a comparison of these results with those of benzimidazole are presented here.