Income modeling using Quantile Functions

Department of Statistics, Cochin University of Science and Technology

Response of Eastern Arabian Sea to Extreme climatic Events with Special Reference to Selected Pelagic Fishes

The thesis attempts to study the changes in oceanographic parameters associated with extreme climatic events,the influence of oceanographic as well as meteorological parameters on fishes.The characteristics of major pelagic fishes of southwest coast of India(Oil sardine and Indian mackerel) have been described here.A description on study area and period of study is also described .The impact of extreme climatic events on the oceanographic variability of Eastern Arabian Sea.The extreme climatic event,the Indian Ocean Dipole associated with EI Nino Southern Oscillation is taken into consideration.The variability in oil sardine and mackerel landings of southwest coast of India during the study period.The trend analysis of the landings has been done and also a prediction model is applied for the landings.The influence of environmental parameters on oil sardine as well as mackerel fishery has been explained .With regression analysis ,the significant relation between environmental parameters and fish landings are also been recognized.The prediction of landings is done with these environmental parameters.

‘Reliability Concepts in Quantile-based Analysis of Lifetime Data

Reliability analysis is a well established branch of statistics that deals with the statistical study of different aspects of lifetimes of a system of components. As we pointed out earlier that major part of the theory and applications in connection with reliability analysis were discussed based on the measures in terms of distribution function. In the beginning chapters of the thesis, we have described some attractive features of quantile functions and the relevance of its use in reliability analysis. Motivated by the works of Parzen (1979), Freimer et al. (1988) and Gilchrist (2000), who indicated the scope of quantile functions in reliability analysis and as a follow up of the systematic study in this connection by Nair and Sankaran (2009), in the present work we tried to extend their ideas to develop necessary theoretical framework for lifetime data analysis. In Chapter 1, we have given the relevance and scope of the study and a brief outline of the work we have carried out. Chapter 2 of this thesis is devoted to the presentation of various concepts and their brief reviews, which were useful for the discussions in the subsequent chapters .In the introduction of Chapter 4, we have pointed out the role of ageing concepts in reliability analysis and in identifying life distributions .In Chapter 6, we have studied the first two L-moments of residual life and their relevance in various applications of reliability analysis. We have shown that the first L-moment of residual function is equivalent to the vitality function, which have been widely discussed in the literature .In Chapter 7, we have defined percentile residual life in reversed time (RPRL) and derived its relationship with reversed hazard rate (RHR). We have discussed the characterization problem of RPRL and demonstrated with an example that the RPRL for given does not determine the distribution uniquely

Halocin SH10 production by an extreme haloarchaeon Natrinema sp. BTSH10 isolated from salt pans of South India

Halobacteria, members of the domain Archaea that live under extremely halophilic conditions, are often considered as dependable source for deriving novel enzymes, novel genes, bioactive compounds and other industrially important molecules. Protein antibiotics have potential for application as preserving agents in food industry, leather industry and in control of infectious bacteria. Halocins are proteinaceous antibiotics synthesized and released into the environment by extreme halophiles, a universal characteristic of halophilic bacteria. Herein, we report the production of halocin (SH10) by an extremely halophilic archeon Natrinema sp. BTSH10 isolated from salt pan of Kanyakumari, Tamilnadu, India and optimization of medium for enhanced production of halocin. It was found that the optimal conditions for maximal halocin production were 42 C, pH 8.0, and 104 h of incubation at 200 rpm with 2% (V/V) inoculum concentration in Zobell’s medium containing 3 M NaCl, Galactose, beef extract, and calcium chloride as additional supplements. Results indicated scope for fermentation production of halocin for probable applications using halophilic archeon Natrinema sp. BTSH10

Quantile based entropy function

Quantile functions are efficient and equivalent alternatives to distribution functions in modeling and analysis of statistical data (see Gilchrist, 2000; Nair and Sankaran, 2009). Motivated by this, in the present paper, we introduce a quantile based Shannon entropy function. We also introduce residual entropy function in the quantile setup and study its properties. Unlike the residual entropy function due to Ebrahimi (1996), the residual quantile entropy function determines the quantile density function uniquely through a simple relationship. The measure is used to define two nonparametric classes of distributions

Quantile based entropy function in past lifetime

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions

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

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions

Quantile based stop-loss transform and its applications

Partial moments are extensively used in actuarial science for the analysis of risks. Since the first order partial moments provide the expected loss in a stop-loss treaty with infinite cover as a function of priority, it is referred as the stop-loss transform. In the present work, we discuss distributional and geometric properties of the first and second order partial moments defined in terms of quantile function. Relationships of the scaled stop-loss transform curve with the Lorenz, Gini, Bonferroni and Leinkuhler curves are developed

A Quantile based analysis of income data

Dept. of Statistics, CUSAT