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A distribuição bivariada de Marshall-Olkin é estendida, relaxando-se a hipótese de choques exponencialmente distribuídos e assumindo-se dependência entre os choques individuais. Abordagem semelhante é considerada para sua versão dual. Representação por meio de cópula, propriedades probabilísticas e de confiabilidade assim como resultados em valores extremos são então obtidos. A propriedade de falta de memória bivariada é estendida assumindo-se uma função de dependência sem memória. Uma nova classe de distribuições caracterizada por essa propriedade estendida é introduzida. Correspondentes interpretações geométricas, procedimentos de construção, representação estocástica, relação com cópula de sobrevivência e propriedades de confiabilidade são derivadas. / Bivariate Marshall-Olkin model, Dual model, Exponential representation, Dependence function, Bivariate aging, Copula, Survival copula, Stochastic order, Bivariate extreme value distribution, Pickands measure, Pickands dependence function, Failure rate, Bivariate hazard gradient, Bivariate lack-of-memory, Residual lifetime vector, Characterization.

A distribuição bivariada de Marshall-Olkin é estendida, relaxando-se a hipótese de choques exponencialmente distribuídos e assumindo-se dependência entre os choques individuais. Abordagem semelhante é considerada para sua versão dual. Representação por meio de cópula, propriedades probabilísticas e de confiabilidade assim como resultados em valores extremos são então obtidos. A propriedade de falta de memória bivariada é estendida assumindo-se uma função de dependência sem memória. Uma nova classe de distribuições caracterizada por essa propriedade estendida é introduzida. Correspondentes interpretações geométricas, procedimentos de construção, representação estocástica, relação com cópula de sobrevivência e propriedades de confiabilidade são derivadas. / Bivariate Marshall-Olkin model, Dual model, Exponential representation, Dependence function, Bivariate aging, Copula, Survival copula, Stochastic order, Bivariate extreme value distribution, Pickands measure, Pickands dependence function, Failure rate, Bivariate hazard gradient, Bivariate lack-of-memory, Residual lifetime vector, Characterization.

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study. / Mathematical Sciences / M. Sc. (Statistics)

Stacy (1962)首先提出廣義伽瑪分配 (generalized gamma distribution)，此分布被廣泛應用於存活分析 (survival analysis) 以及可靠度 (reliability) 中壽命時間的資料描述。事實上，像是指數分配 (exponential distribution)、韋伯分配 (Weibull distribution) 以及伽瑪分配 (gamma distribution) 都是廣義伽瑪分配的一個特例。 Bologna (1987)提出一個特殊的雙變量廣義伽瑪分配 (bivariate generalized gamma distribution) 可以經由雙變量常態分配 (bivariate normal distribution) 所推得。我們根據他的想法，提出多變量廣義伽瑪分配可以經由多變量常態分配所推得。在過去的研究中，學者們做了許多有關雙變量伽瑪分配。當我們提到雙變量常態分配，由於其分配的型式為唯一的，所以沒人任何人對其分配的型式有疑問。然而，雙變量伽瑪分配卻有很多不同的型式。 在這篇論文中的架構如下。在第二章中，我們介紹並討論雙變量廣義伽瑪分配可以經由雙變量常態分配所推得，接著推導參數估計以及介紹模擬的程序。在第三章中，我們介紹一些對稱以及非對稱的雙變量伽瑪分配，接著拓展到雙變量廣義伽瑪分配，有關參數的估計以及模擬結果也將在此章中討論。在第三章最後，我們建構參數的敏感度分析 (sensitivity analysis)。最後，在第四章中，我們陳述結論以及未來研究方向。 / The generalized gamma distribution was introduced by Stacy (1962). This distribution is useful to describe lifetime data when conducting survival analysis and reliability. In fact, it includes the widely used exponential, Weibull, and gamma distributions as special cases. Bologna (1987) showed that a special bivariate genenralized gamma distribution can be derived from a bivariate normal distribution. Follow his idea, we show that a multivariate generalized gamma distribution can be derived from a multivariate normal distribution. In the past, researchers spend much time in working on a bivariate gamma distribution. When a bivariate normal distribution is mentioned, no one feels puzzled about its form, since it has only one form. However, there are various forms of bivariate gamma distributions. In this paper is as following. In Chapter 2, we introduce and discuss the bivariate generalized gamma distribution, then the multivariate generalized gamma distribution is derived. We also develop parameters estimation and simulation procedure. In Chapter 3, we introduce some symmetrical and asymmetrical bivariate gamma distributions, then they are extended to the bivariate generalized gamma distributions. Problems of parameters estimation and simulation results are also discussed in Chapter 3. Besides, sensitivity analyses of parameters estimation are conducted. Finally, we state conclusion and future work in Chapter 4.

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study. / Mathematical Sciences / M. Sc. (Statistics)

This thesis consists of four papers concerning modelling of count data and tourism demand. For three of the papers the focus is on the integer-valued autoregressive moving average model class (INARMA), and especially on the ENAR(l) model. The fourth paper studies the interaction between households' choice of number of leisure trips and number of overnight stays within a bivariate count data modelling framework. Paper [I] extends the basic INAR(1) model to enable more flexible and realistic empirical economic applications. The model is generalized by relaxing some of the model's basic independence assumptions. Results are given in terms of first and second conditional and unconditional order moments. Extensions to general INAR(p), time-varying, multivariate and threshold models are also considered. Estimation by conditional least squares and generalized method of moments techniques is feasible. Monte Carlo simulations for two of the extended models indicate reasonable estimation and testing properties. An illustration based on the number of Swedish mechanical paper and pulp mills is considered. Paper[II] considers the robustness of a conventional Dickey-Fuller (DF) test for the testing of a unit root in the INAR(1) model. Finite sample distributions for a model with Poisson distributed disturbance terms are obtained by Monte Carlo simulation. These distributions are wider than those of AR(1) models with normal distributed error terms. As the drift and sample size, respectively, increase the distributions appear to tend to T-2) and standard normal distributions. The main results are summarized by an approximating equation that also enables calculation of critical values for any sample and drift size. Paper[III] utilizes the INAR(l) model to model the day-to-day movements in the number of guest nights in hotels. By cross-sectional and temporal aggregation an INARMA(1,1) model for monthly data is obtained. The approach enables easy interpretation and econometric modelling of the parameters, in terms of daily mean check-in and check-out probability. Empirically approaches accounting for seasonality by dummies and using differenced series, as well as forecasting, are studied for a series of Norwegian guest nights in Swedish hotels. In a forecast evaluation the improvements by introducing economic variables is minute. Paper[IV] empirically studies household's joint choice of the number of leisure trips and the total night to stay on these trips. The paper introduces a bivariate count hurdle model to account for the relative high frequencies of zeros. A truncated bivariate mixed Poisson lognormal distribution, allowing for both positive as well as negative correlation between the count variables, is utilized. Inflation techniques are used to account for clustering of leisure time to weekends. Simulated maximum likelihood is used as estimation method. A small policy study indicates that households substitute trips for nights as the travel costs increase. / <p>Härtill 4 uppsatser.</p> / digitalisering@umu

The purpose of this study was to examine the effects of parenting training on the acquisition of parenting skills and its impact on self-esteem of incarcerated mothers. The program under study is the "Mothers Inside Loving Kids" (M.I.L.K.) program, which is a holistic training/visitation program designed for incarcerated mothers.Study participants included 40 volunteer incarcerated mothers at the Virginia Correctional Center for women. The treatment group consisted of 20 participants who were already involved in the "M.I.L.K." program. The comparison group was made up of 20 mothers who were on the waiting list for the program due to the lack of space. All participants were administered a battery of pre-tests and post-tests. Instruments utilized for the study included the Adult-Adolescent Parenting Inventory (AAPI), the Nurturing Quiz, the Index of Self Esteem (ISE), and a participant satisfaction survey.Bivariate analyses were used to test the difference between pre-test and post-test mean scores. Both parametric and non-parametric tests were conducted to determine if change scores revealed significant differences. Using independent t-tests to determine if there were significant differences between treatment and comparison groups on change scores, no significant differences were noted. However, in reviewing the direction of change scores for the two groups, the treatment group did show changes in the desired direction in four areas. Specifically, positive directional change occurred on the "Lack of Empathy for the Child" sub-scale, the "Belief in Corporal Punishment" sub-scale, the "Reversing Family Roles" sub-scale, and on the "Nurturing Quiz."Using the Wilcoxon non-parametric test, one measure revealed statistically significant differences between pre-test and post-test scores. Specifically, participants in the treatment group revealed significantly higher scores on the "Nurturing Quiz" at post-testing from pre-testing (z = -2.81, p = .005). This indicates an overall increase in knowledge about positive child management techniques. No significant pre-test to post-test differences were noted in any of the remaining areas under study. However, positive directional change scores were noted in the three different areas of "Inappropriate Expectations of the Child", "Nurturing", and "Self-Esteem."Overall, the findings suggest that the M.I.L.K. Program training positively impacts parenting techniques. Self-esteem appears more difficult to impact.