Modelling and Analysis of Bivariate Lifetime Data using Reversed Hazard Rates

Department of Statistics, Cochin University of Science and Technology

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

A Study on the Reversed Lack of Memory Property and its Generalizations

In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ”addition”. In particular an associative, binary operator ” * ” is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

‘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

Nonparametric Estimation of Survivor Function in Bivariate Competing Risk Models’

So far, in the bivariate set up, the analysis of lifetime (failure time) data with multiple causes of failure is done by treating each cause of failure separately. with failures from other causes considered as independent censoring. This approach is unrealistic in many situations. For example, in the analysis of mortality data on married couples one would be interested to compare the hazards for the same cause of death as well as to check whether death due to one cause is more important for the partners’ risk of death from other causes. In reliability analysis. one often has systems with more than one component and many systems. subsystems and components have more than one cause of failure. Design of high-reliability systems generally requires that the individual system components have extremely high reliability even after long periods of time. Knowledge of the failure behaviour of a component can lead to savings in its cost of production and maintenance and. in some cases, to the preservation of human life. For the purpose of improving reliability. it is necessary to identify the cause of failure down to the component level. By treating each cause of failure separately with failures from other causes considered as independent censoring, the analysis of lifetime data would be incomplete. Motivated by this. we introduce a new approach for the analysis of bivariate competing risk data using the bivariate vector hazard rate of Johnson and Kotz (1975).

Development of a Biometric Personal Authentication System Based on Fingerprint and Speech

Biometrics deals with the physiological and behavioral characteristics of an individual to establish identity. Fingerprint based authentication is the most advanced biometric authentication technology. The minutiae based fingerprint identification method offer reasonable identification rate. The feature minutiae map consists of about 70-100 minutia points and matching accuracy is dropping down while the size of database is growing up. Hence it is inevitable to make the size of the fingerprint feature code to be as smaller as possible so that identification may be much easier. In this research, a novel global singularity based fingerprint representation is proposed. Fingerprint baseline, which is the line between distal and intermediate phalangeal joint line in the fingerprint, is taken as the reference line. A polygon is formed with the singularities and the fingerprint baseline. The feature vectors are the polygonal angle, sides, area, type and the ridge counts in between the singularities. 100% recognition rate is achieved in this method. The method is compared with the conventional minutiae based recognition method in terms of computation time, receiver operator characteristics (ROC) and the feature vector length. Speech is a behavioural biometric modality and can be used for identification of a speaker. In this work, MFCC of text dependant speeches are computed and clustered using k-means algorithm. A backpropagation based Artificial Neural Network is trained to identify the clustered speech code. The performance of the neural network classifier is compared with the VQ based Euclidean minimum classifier. Biometric systems that use a single modality are usually affected by problems like noisy sensor data, non-universality and/or lack of distinctiveness of the biometric trait, unacceptable error rates, and spoof attacks. Multifinger feature level fusion based fingerprint recognition is developed and the performances are measured in terms of the ROC curve. Score level fusion of fingerprint and speech based recognition system is done and 100% accuracy is achieved for a considerable range of matching threshold

Applying Data mining using Statistical Techniques for Career Selection

For years, choosing the right career by monitoring the trends and scope for different career paths have been a requirement for all youngsters all over the world. In this paper we provide a scientific, data mining based method for job absorption rate prediction and predicting the waiting time needed for 100% placement, for different engineering courses in India. This will help the students in India in a great deal in deciding the right discipline for them for a bright future. Information about passed out students are obtained from the NTMIS ( National technical manpower information system ) NODAL center in Kochi, India residing in Cochin University of science and technology

Some Properties of Weighted Distributions in the Context of Repairable Systems

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables

Characterizations of bivariate models using dynamic Kullback–Leibler discrimination measures

In this paper, the residual Kullback–Leibler discrimination information measure is extended to conditionally specified models. The extension is used to characterize some bivariate distributions. These distributions are also characterized in terms of proportional hazard rate models and weighted distributions. Moreover, we also obtain some bounds for this dynamic discrimination function by using the likelihood ratio order and some preceding results.

Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specifiedmodels and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order

Identifying Decisive Features for Distinctive Analysis of Writings in Malayalam

This paper presents a writer identification scheme for Malayalam documents. As the accomplishment rate of a scheme is highly dependent on the features extracted from the documents, the process of feature selection and extraction is highly relevant. The paper describes a set of novel features exclusively for Malayalam language. The features were studied in detail which resulted in a comparative study of all the features. The features are fused to form the feature vector or knowledge vector. This knowledge vector is then used in all the phases of the writer identification scheme. The scheme has been tested on a test bed of 280 writers of which 50 writers having only one page, 215 writers with at least 2 pages and 15 writers with at least 4 pages. To perform a comparative evaluation of the scheme the test is conducted using WD-LBP method also. A recognition rate of around 95% was obtained for the proposed approach

β-glucosidases from Aspergillus unguis NII 08123: Molecular characterization, properties and applications

Lignocellulosic biomass is probably the best alternative resource for biofuel production and it is composed mainly of cellulose, hemicelluloses and lignin. Cellulose is the most abundant among the three and conversion of cellulose to glucose is catalyzed by the enzyme cellulase. Cellulases are groups of enzymes act synergistically upon cellulose to produce glucose and comprise of endoglucanase, cellobiohydrolase and β-glucosidase. β -glucosidase assumes great importance due to the fact that it is the rate limiting enzyme. Endoglucanases (EG) produces nicks in the cellulose polymer exposing reducing and non reducing ends, cellobiohydrolases (CBH) acts upon the reducing or non reducing ends to liberate cellobiose units, and β - glucosidases (BGL) cleaves the cellobiose to liberate glucose completing the hydrolysis. . β -glucosidases undergo feedback inhibition by their own product- β glucose, and cellobiose which is their substrate. Few filamentous fungi produce glucose tolerant β - glucosidases which can overcome this inhibition by tolerating the product concentration to a particular threshold. The present study had targeted a filamentous fungus producing glucose tolerant β - glucosidase which was identified by morphological as well as molecular method. The fungus showed 99% similarity to Aspergillus unguis strain which comes under the Aspergillus nidulans group where most of the glucose tolerant β -glucosidase belongs. The culture was designated the strain number NII 08123 and was deposited in the NII culture collection at CSIR-NIIST. β -glucosidase multiplicity is a common occurrence in fungal world and in A.unguis this was demonstrated using zymogram analysis. A total 5 extracellular isoforms were detected in fungus and the expression levels of these five isoforms varied based on the carbon source available in the medium. Three of these 5 isoforms were expressed in higher levels as identified by the increased fluorescence (due to larger amounts of MUG breakdown by enzyme action) and was speculated to contribute significantly to the total _- β glucosidase activity. These isoforms were named as BGL 1, BGL3 and BGL 5. Among the three, BGL5 was demonstrated to be the glucose tolerant β -glucosidase and this was a low molecular weight protein. Major fraction was a high molecular weight protein but with lesser tolerance to glucose. BGL 3 was between the two in both activity and glucose tolerance.121 Glucose tolerant .β -glucosidase was purified and characterized and kinetic analysis showed that the glucose inhibition constant (Ki) of the protein is 800mM and Km and Vmax of the enzyme was found to be 4.854 mM and 2.946 mol min-1mg protein-1respectively. The optimumtemperature was 60°C and pH 6.0. The molecular weight of the purified protein was ~10kDa in both SDS as well as Native PAGE indicating that the glucose tolerant BGL is a monomeric protein.The major β -glucosidase, BGL1 had a pH and temperature optima of 5.0 and 60 °C respectively. The apparent molecular weight of the Native protein is 240kDa. The Vmax and Km was 78.8 mol min-1mg protein-1 and 0.326mM respectively. Degenerate primers were designed for glycosyl hydrolase families 1, 3 and 5 and the BGL genes were amplified from genomic DNA of Aspergillus unguis. The sequence analyses performed on the amplicons results confirmed the presence of all the three genes. Amplicon with a size of ~500bp was sequenced and which matched to a GH1 –BGL from Aspergillus oryzae. GH3 degenerate primers producing amplicons were sequenced and the sequences matched to β - glucosidase of GH3 family from Aspergillus nidulans and Aspergillus acculateus. GH5 degenerate primers also gave amplification and sequencing results indicated the presence of GH5 family BGL gene in the Aspergillus unguis genomic DNA.From the partial gene sequencing results, specific as well as degenerate primers were designed for TAIL PCR. Sequencing results of the 1.0 Kb amplicon matched Aspergillus nidulans β -glucosidase gene which belongs to the GH1 family. The sequence mainly covered the N-Terminal region of the matching peptide. All the three BGL proteins ie. BGL1, BGL3 and BGL5 were purified by chromatography an electro elution from Native PAGE gels and were subjected to MALDI-TOF mass spectrometric analysis. The results showed that BGL1 peptide mass matched to . β -glucosidase-I of Aspergillus flavus which is a 92kDa protein with 69% protein coverage. The glucose tolerant β -glucosidase BGL5 mass matched to the catalytic C-terminal domain of β -glucosidase-F from Emericella nidulans, but the protein coverage was very low compared to the size of the Emericella nidulans protein. While comparing the size of BGL5 from Aspergillus unguis, the protein sequence coverage is more than 80%. BGL F is a glycosyl hydrolase family 3 protein.The properties of BGL5 seem to be very unique, in that it is a GH3 β -glucosidase with a very low molecular weight of ~10kDa and at the same time having catalytic activity and glucose 122 tolerance which is as yet un-described in GH β -glucosidases. The occurrence of a fully functional 10kDA protein with glucose tolerant BGL activity has tremendous implications both from the points of understanding the structure function relationships as well as for applications of BGL enzymes. BGL-3 showed similarity to BGL1 of Aspergillus aculateus which was another GH3 β -glucosidase. It may be noted that though PCR could detect GH1, GH3 and GH5 β-glucosidases in the fungus, the major isoforms BGL1 BGL3 and BGL5 were all GH3 family enzymes. This would imply that β-glucosidases belonging to other families may also co-exist in the fungus and the other minor isoforms detected in zymograms may account for them. In biomass hydrolysis, GT-BGL containing BGL enzyme was supplemented to cellulase and the performances of blends were compared with a cocktail where commercial β- glucosidase was supplemented to the biomass hydrolyzing enzyme preparation. The cocktail supplemented with A unguis BGL preparation yielded 555mg/g sugar in 12h compared to the commercial enzyme preparation which gave only 333mg/g in the same period and the maximum sugar yield of 858 mg/g was attained in 36h by the cocktail containing A. unguis BGL. While the commercial enzyme achieved almost similar sugar yield in 24h, there was rapid drop in sugar concentration after that, indicating probably the conversion of glucose back to di-or oligosaccharides by the transglycosylation activity of the BGl in that preparation. Compared this, the A.unguis enzyme containing preparation supported peak yields for longer duration (upto 48h) which is important for biomass conversion to other products since the hydrolysate has to undergo certain unit operations before it goes into the next stage ie – fermentation in any bioprocesses for production of either fuels or chemicals.. Most importantly the Aspergillus unguis BGL preparation yields approximately 1.6 fold increase in the sugar release compared to the commercial BGL within 12h of time interval and 2.25 fold increase in the sugar release compared to the control ie. Cellulase without BGL supplementation. The current study therefore leads to the identification of a potent new isolate producing glucose tolerant β - glucosidase. The organism identified as Aspergillus unguis comes under the Aspergillus nidulans group where most of the GT-BGL producers belong and the detailed studies showed that the glucose tolerant β -glucosidase was a very low molecular weight protein which probably belongs to the glycosyl hydrolase family 3. Inhibition kinetic studies helped to understand the Ki and it is the second highest among the nidulans group of Aspergilli. This has promoted us for a detailed study regarding the mechanism of glucose tolerance. The proteomic 123 analyses clearly indicate the presence of GH3 catalytic domain in the protein. Since the size of the protein is very low and still its active and showed glucose tolerance it is speculated that this could be an entirely new protein or the modification of the existing β -glucosidase with only the catalytic domain present in it. Hydrolysis experiments also qualify this BGL, a suitable candidate for the enzyme cocktail development for biomass hydrolysis