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

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

Habitat ecology and food and feeding of the herring bow crab Varuna litterata (Fabricius, 1798) of Cochin backwaters, Kerala, India

Habitat ecology and food and feeding of the herring bow crab, Varuna litterata of Cochin Backwaters, Kerala, India were investigated for a period of one year (April 2011-March 2012). Among the 15 stations surveyed, the crabs were found to occur only in 4 stations, which had a close proximity to the sea. Sediment analysis of the stations revealed that the substratum of these stations is sandy in nature and is rich in organic carbon content (0.79% to 1.07%). These estuarine crabs is euryhaline and are found to be distributed in areas with a sandy substratum, higher organic carbon content and more tidal influx. The stomach contents analysis of crabs examined showed that their diet included crustacean remains, plants, sand and debris, fishes, miscellaneous group and unidentified matter. In adults and sub-adults, crustaceans formed the dominant food group, while in juveniles, sand and debris formed the dominant group. From the present study, V. litterata was found to be a predatory omnivore capable of ingesting both animal and plant tissues

Brachyuran Crabs of Cochin Backwaters- Diversity, Habitat Ecology and Systematics, with special emphasis to Genus Scylla

Among the decapod crustaceans, brachyuran crabs or the true crabs occupy a very significant position due to their ecological and economic value. Crabs support a sustenance fishery in India, even though their present status is not comparable to that of shrimps and lobsters. They are of great demand in the domestic market as well as in the foreign markets. In addition to this, brachyuran crabs are of great ecological importance. They form the conspicuous members of the mangrove ecosystems and play a significant role in detritus formation, nutrient recycling and dynamics of the ecosystem. Considering all these factors, crabs are often considered to be the keystone species of the mangrove ecosystem. Though several works have been undertaken on brachyuran crabs world –wide as well as within the country, reports on the brachyuran crabs of Kerala waters are very scanty. Most of the studies done on brachyuran fauna were from the east coast of India and a very few works from the west coast. Among the edible crabs, mud crabs belonging to genus Scylla forms the most important due to their large size and taste. They are being exported on a large scale to the foreign markets like Singapore, Malaysia and Hong Kong. Kerala is the biggest supplier of live mud crabs and Chennai is the major centre of live mud crab export. However, there exists considerable confusion regarding the identification of mud crabs because of the subtle morphological differences between the species.In this context, an extensive study was undertaken on the brachyuran fauna of Cochin Backwaters, Kerala, India, to have a basic knowledge on their diversity, habitat preference and systematics. The study provides an attempt to resolve the confusion pertaining in the species identification of mud crabs belonging to Genus Scylla. Diversity study revealed the occurrence of 23 species of brachyuran crabs belonging to 16 genera and 8 families in the study area Cochin Backwaters. Among the families, the highest number of species was recorded from Family Portunidae .Among the 23 crab species enlisted from the Cochin backwaters, 5 species are of commercial importance and contribute a major share to the crustacean fishery of the Cochin region. It was observed that, the Cochin backwaters are invaded by certain marine migrant species during the Post monsoon and Pre monsoon periods and they are found to disappear with the onset of monsoon. The study reports the occurrence of the ‘herring bow crab’ Varuna litterata in the Cochin backwaters for the first time. Ecological studies showed that the substratum characteristics influence the occurrence, distribution and abundance of crabs in the sampling stations rather than water quality parameters. The variables which affected the crab distribution the most were Salinity, moisture content in the sediment, organic carbon and the sediment texture. Besides the water and sediment quality parameters, the most important factor influencing the distribution of crabs is the presence of mangroves. The study also revealed that most of the crabs encountered from the study area preferred a muddy substratum, with high organic carbon content and high moisture content. In the present study, an identification key is presented for the brachyuran crabs occurring along the study area the Cochin backwaters and the associated mangrove patches, taking into account the morphological characters coupled with the structure of third maxillipeds, first pleopods of males and the shape of male abdomen. Morphological examination indicated the existence of a morphotype which is comparable with the morphological features of S. tranquebarica, the morphometric study and the molecular analyses confirmed the non existence of S. tranquebarica in the Cochin backwaters.