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.

Implied Hazard Rates Analysis Through Brazilian Corporate Debt

No Brasil, o mercado de crédito corporativo ainda é sub-aproveitado. A maioria dos participantes não exploram e não operam no mercado secundário, especialmente no caso de debêntures. Apesar disso, há inúmeras ferramentas que poderiam ajudar os participantes do mercado a analisar o risco de crédito e encorajá-los a operar esses riscos no mercado secundário. Essa dissertação introduz um modelo livre de arbitragem que extrai a Perda Esperada Neutra ao Risco Implícita nos preços de mercado. É uma forma reduzida do modelo proposto por Duffie and Singleton (1999) e modela a estrutura a termo das taxas de juros através de uma Função Constante por Partes. Através do modelo, foi possível analisar a Curva de Perda Esperada Neutra ao Risco Implícita através dos diferentes instrumentos de emissores corporativos brasileiros, utilizando Títulos de Dívida, Swaps de Crédito e Debêntures. Foi possível comparar as diferentes curvas e decidir, em cada caso analisado, qual a melhor alternativa para se tomar o risco de crédito da empresa, via Títulos de Dívida, Debêntures ou Swaps de Crédito.

Institutional specifics and unemployment insurance eligibility in Canada : how sensitive are employment duration effects?

The paper examines the influence of unemployment insurance on the duration of employment spells in Canada using the 1988–90 Labour Market Activity Survey. The primary focus of the paper is to evaluate whether estimated UI effects are sensitive to the degree to which institutional rules and regulations governing UI eligibility and entitlement are explicitly modelled. The key result of the paper is that it is indeed important to allow for institutional detail when estimating unemployment insurance effects. Estimates using simple proxies for eligibility indicate small, often insignificant UI effects. The size and significance of the effects rise as more realistic versions of the variables are adopted. The estimates using the eligibility variables incorporating the greatest level of institutional detail suggest that a jump in the hazard rate by a factor of 2.3 may not be an unreasonable estimate of the effect.

Are lemons really hot potatoes?

We model the hazard rate for car ownership spells. Our model allows us to distinguish among different types of adverse selection effects by observing the type of unobserved heterogeneity across owners of the same car. Our empirical results strongly suggest that there is a lemons effect because there is significant unobserved heterogeneity. However, they also suggest that the lemons effect is caused by the first owner rather than the manufacturer. Had the manufacturer created the lemon, the unobserved heterogeneity would be positively correlated over all owners of a given car. Instead we observe a negative correlation between the unobserved heterogeneity term for the first owner and the unobserved heterogeneity term for subsequent owners. © 2008 Elsevier B.V. All rights reserved.

Essays on the Economics of Intellectual Property Rights

Väitöskirjassani tarkastelen informaatiohyödykkeiden ja tekijänoikeuksien taloustiedettä kahdesta eri perspektiivistä. Niistä ensimmäinen kuuluu endogeenisen kasvuteorian alaan. Väitöskirjassani yleistän ”pool of knowledge” -tyyppisen endogeenisen kasvumallin tilanteeseen, jossa patentoitavissa olevalla innovaatiolla on minimikoko, ja jossa uudenlaisen tuotteen patentoinut yritys voi menettää monopolinsa tuotteeseen jäljittelyn johdosta. Mallin kontekstissa voidaan analysoida jäljittelyn ja innovaatioilta vaaditun ”minimikoon” vaikutuksia hyvinvointiin ja talouskasvuun. Kasvun maksimoiva imitaation määrä on mallissa aina nolla, mutta hyvinvoinnin maksimoiva imitaation määrä voi olla positiivinen. Talouskasvun ja hyvinvoinnin maksimoivalla patentoitavissa olevan innovaation ”minimikoolla” voi olla mikä tahansa teoreettista maksimia pienempi arvo. Väitöskirjani kahdessa jälkimmäisessä pääluvussa tarkastelen informaatiohyödykkeiden kaupallista piratismia mikrotaloustieteellisen mallin avulla. Informaatiohyödykkeistä laittomasti tehtyjen kopioiden tuotantokustannukset ovat pienet, ja miltei olemattomat silloin kun niitä levitetään esimerkiksi Internetissä. Koska piraattikopioilla on monta eri tuottajaa, niiden hinnan voitaisiin mikrotaloustieteen teorian perusteella olettaa laskevan melkein nollaan, ja jos näin kävisi, kaupallinen piratismi olisi mahdotonta. Mallissani selitän kaupallisen piratismin olemassaolon olettamalla, että piratismista saatavan rangaistuksen uhka riippuu siitä, kuinka monille kuluttajille piraatti tarjoaa laittomia hyödykkeitä, ja että se siksi vaikuttaa piraattikopioiden markkinoihin mainonnan kustannuksen tavoin. Kaupallisten piraattien kiinteiden kustannusten lisääminen on mallissani aina tekijänoikeuksien haltijan etujen mukaista, mutta ”mainonnan kustannuksen” lisääminen ei välttämättä ole, vaan se saattaa myös alentaa laillisten kopioiden myynnistä saatavia voittoja. Tämä tulos poikkeaa vastaavista aiemmista tuloksista sikäli, että se pätee vaikka tarkasteltuihin informaatiohyödykkeisiin ei liittyisi verkkovaikutuksia. Aiemmin ei-kaupallisen piratismin malleista on usein johdettu tulos, jonka mukaan informaatiohyödykkeen laittomat kopiot voivat kasvattaa laillisten kopioiden myynnistä saatavia voittoja jos laillisten kopioiden arvo niiden käyttäjille riippuu siitä, kuinka monet muut kuluttajat käyttävät samanlaista hyödykettä ja jos piraattikopioiden saatavuus lisää riittävästi laillisten kopioiden arvoa. Väitöskirjan viimeisessä pääluvussa yleistän mallini verkkotoimialoille, ja tutkin yleistämäni mallin avulla sitä, missä tapauksissa vastaava tulos pätee myös kaupalliseen piratismiin.

Survival analysis of adult tuberculosis disease

Background: We conducted a survival analysis of all the confirmed cases of Adult Tuberculosis (TB) patients treated in Cork-City, Ireland. The aim of this study was to estimate Survival time (ST), including median time of survival and to assess the association and impact of covariates (TB risk factors) to event status and ST. The outcome of the survival analysis is reported in this paper. Methods: We used a retrospective cohort study research design to review data of 647 bacteriologically confirmed TB patients from the medical record of two teaching hospitals. Mean age 49 years (Range 18–112). We collected information on potential risk factors of all confirmed cases of TB treated between 2008–2012. For the survival analysis, the outcome of interest was ‘treatment failure’ or ‘death’ (whichever came first). A univariate descriptive statistics analysis was conducted using a non- parametric procedure, Kaplan -Meier (KM) method to estimate overall survival (OS), while the Cox proportional hazard model was used for the multivariate analysis to determine possible association of predictor variables and to obtain adjusted hazard ratio. P value was set at <0.05, log likelihood ratio test at >0.10. Data were analysed using SPSS version 15.0. Results: There was no significant difference in the survival curves of male and female patients. (Log rank statistic = 0.194, df = 1, p = 0.66) and among different age group (Log rank statistic = 1.337, df = 3, p = 0.72). The mean overall survival (OS) was 209 days (95%CI: 92–346) while the median was 51 days (95% CI: 35.7–66). The mean ST for women was 385 days (95%CI: 76.6–694) and for men was 69 days (95%CI: 48.8–88.5). Multivariate Cox regression showed that patient who had history of drug misuse had 2.2 times hazard than those who do not have drug misuse. Smokers and alcohol drinkers had hazard of 1.8 while patients born in country of high endemicity (BICHE) had hazard of 6.3 and HIV co-infection hazard was 1.2. Conclusion: There was no significant difference in survival curves of male and female and among age group. Women had a higher ST compared to men. But men had a higher hazard rate compared to women. Anti-TNF, immunosuppressive medication and diabetes were found to be associated with longer ST, while alcohol, smoking, RICHE, BICHE was associated with shorter ST.

Firms survival and international trade: The impact of exports and imports

Double Degree. A Work Project presented as part of the requirements for the Award of a Masters in Management from Nova School of Business and Economics and Maastricht University.

Determinants of bankruptcy protection duration for Canadian firms

The present thesis examines the determinants of the bankruptcy protection duration for Canadian firms. Using a sample of Canadian firms that filed for bankruptcy protection between the calendar years 1992 and 2009, we fmd that the firm age, the industry adjusted operating margin, the default spread, the industrial production growth rate or the interest rate are influential factors on determining the length of the protection period. Older firms tend to stay longer under protection from creditors. As older firms have more complicated structures and issues to settle, the risk of exiting soon the protection (the hazard rate) is small. We also find that firms that perform better than their benchmark as measured by the industry they belong to, tend to leave quickly the bankruptcy protection state. We conclude that the fate of relatively successful companies is determined faster. Moreover, we report that it takes less time to achieve a final solution to firms under bankrupt~y when the default spread is low or when the appetite for risk is high. Conversely, during periods of high default spreads and flight for quality, it takes longer time to resolve the bankruptcy issue. This last finding may suggest that troubled firms should place themselves under protection when spreads are low. However, this ignores the endogeneity issue: high default spread may cause and incidentally reflect higher bankruptcy rates in the economy. Indeed, we find that bankruptcy protection is longer during economic downturns. We explain this relation by the natural increase in default rate among firms (and individuals) during economically troubled times. Default spreads are usually larger during these harsh periods as investors become more risk averse since their wealth shrinks. Using a Log-logistic hazard model, we also fmd that firms that file under the Companies' Creditors Arrangement Act (CCAA) protection spend longer time restructuring than firms that filed under the Bankruptcy and Insolvency Act (BIA). As BIA is more statutory and less flexible, solutions can be reached faster by court orders.

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).

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