Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

Ruthenium complexes of Schiff base ligands as efficient catalysts for catechol–hydrogen peroxide reaction

Zeolite Y-encapsulated ruthenium(III) complexes of Schiff bases derived from 3-hydroxyquinoxaline-2-carboxaldehyde and 1,2- phenylenediamine, 2-aminophenol, or 2-aminobenzimidazole (RuYqpd, RuYqap and RuYqab, respectively) and the Schiff bases derived from salicylaldehyde and 1,2-phenylenediamine, 2-aminophenol, or 2-aminobenzimidazole (RuYsalpd, RuYsalap and RuYsalab, respectively) have been prepared and characterized. These complexes, except RuYqpd, catalyze catechol oxidation by H2O2 selectively to 1,2,4-trihydroxybenzene. RuYqpd is inactive. A comparative study of the initial rates and percentage conversion of the reaction was done in all cases. Turn over frequency of the catalysts was also calculated. The catalytic activity of the complexes is in the order RuYqap > RuYqab for quinoxaline-based complexes and RuYsalap > RuYsalpd > RuYsalab for salicylidene-based complexes. The reaction is believed to proceed through the formation of a Ru(V) species.

Wet peroxide oxidation of phenol over mixed pillared montmorillonites

Wet peroxide oxidation (WPO) of phenol is an effective means for the production of diphenols, which are of great industrial importance. An added advantage of this method is the removal of phenol from wastewater effluents. Hydroxylation of phenol occurs efficiently over mixed iron aluminium pillared montmorillonites. An initial induction period is noticed in all cases. A thorough study on the reaction variables suggests free radical mechanism for the reaction.

Influence of residual cations (Na+, K+ and Mg2+) in the alkylation activity of benzene with 1-octene over rare earth metal ion exchanged FAU–Y zeolite

The effect of residual cations in rare earth metal modified faujasite–Y zeolite has been monitored using magic angle spinning NMR spectral analysis and catalytic activity studies. The second metal ions being used are Na+, K+ and Mg+. From a comparison of the spectra of different samples, it is concluded that potassium and magnesium exchange causes a greater downfield shift in the 29Si NMR peaks. Also, lanthanum exchanged samples show migration behavior from large cages to small cages, which causes the redistribution of second counter cations. It is also observed that Mg2+ causes the most effective migration of lanthanum ions due to its greater charge. The prepared systems were effectively employed for the alkylation of benzene with 1-octene in the vapor phase. From the deactivation studies it is observed that the as-exchanged zeolites possess better stability towards reaction condition over the pure HFAU zeolite.

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto 11 and beta distributions. Further, we generalize the identities for fire Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in file context of lengthbiased models are also explored

Dynamic cumulative residual Renyi’s entropy

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon’s entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi’s entropy, and study its properties.We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models

Rényi’s residual entropy: A quantile approach

In the present paper, we introduce a quantile based Rényi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Rényi’s entropy function, the quantile version uniquely determines the distribution