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BackgroundThe growing amount of high dimensional biomolecular data has spawned new statistical and computational models for risk prediction and disease classification. Yet, many of these methods do not yield biologically interpretable models, despite offering high classification accuracy. An exception, the top-scoring pair (TSP) algorithm derives parameter-free, biologically interpretable single pair decision rules that are accurate and robust in disease classification. However, standard TSP methods do not accommodate covariates that could heavily influence feature selection for the top-scoring pair. Herein, we propose a covariate-adjusted TSP method, which uses residuals from a regression of features on the covariates for identifying top scoring pairs. We conduct simulations and a data application to investigate our method, and compare it to existing classifiers, LASSO and random forests.ResultsOur simulations found that features that were highly correlated with clinical variables had high likelihood of being selected as top scoring pairs in the standard TSP setting. However, through residualization, our covariate-adjusted TSP was able to identify new top scoring pairs, that were largely uncorrelated with clinical variables. In the data application, using patients with diabetes (n = 977) selected for metabolomic profiling in the Chronic Renal Insufficiency Cohort (CRIC) study, the standard TSP algorithm identified (valine-betaine, dimethyl-arg) as the top-scoring metabolite pair for classifying diabetic kidney disease (DKD) severity, whereas the covariate-adjusted TSP method identified the pair (pipazethate, octaethylene glycol) as top-scoring. Valine-betaine and dimethyl-arg had, respectively, ≥ 0.4 absolute correlation with urine albumin and serum creatinine, known prognosticators of DKD. Thus without covariate-adjustment the top-scoring pair largely reflected known markers of disease severity, whereas covariate-adjusted TSP uncovered features liberated from conf

In this paper, a new distribution of the Muth-generated family is introduced by considering the Pareto model as baseline with the goal of having increased flexibility and improved goodness of fit in terms of studying tail characteristics. Maximum likelihood estimated parameters of the distribution were found to be consistent and asymptotically unbiased. From a practical point of view, it is shown that the proposed distribution is more flexible than some common statistical distributions. In particular, the proposed model proved to fit well into unimodal data structures. Some mathematical properties were derived, and characterization investigated by truncated first moment where a product of reverse hazard rate and another function of the truncated point is considered. Other characterizations by order statistics and upper record values based on the characterization by the first truncated moment were also established.

For a sample from GEM distribution considered as a random discrete distribution of positive integers, there are probably unobserved less positive integers than the maximum sample. The number of these integers follows a mixed Poisson distribution. Here, we provide a simple proof of the convergence in distribution of this number. Similarly, its asymptotic distribution is a mixed Poisson. We derived the upper bounds for the total variation between the finite and asymptotic distributions. These distributions are illustrated by examples; the related total values are provided in table 1.

This article explores U-Statistics as a tool for testing conditional correlation between two multivariate sources with respect to a potential confounder. The proposed approach is effectively an instance of weighted U-Statistics and does not impose any statistical model on the processed data, in contrast to other well-known techniques that assume Gaussianity. By avoiding determinants and inverses, the method presented displays promising robustness in small-sample regimes. Its performance is evaluated numerically through its MSE and ROC curves., Peer Reviewed, Postprint (author's final draft)

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size., CC BY 4.0Correspondence: ieva.meidute-kavaliauskiene@vilniustech.ltFunding: This research received no external funding

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size., CC BY 4.0Correspondence: ieva.meidute-kavaliauskiene@vilniustech.ltFunding: This research received no external funding

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.

For a sample from GEM distribution considered as a random discrete distribution of positive integers, there are probably unobserved less positive integers than the maximum sample. The number of these integers follows a mixed Poisson distribution. Here, we provide a simple proof of the convergence in distribution of this number. Similarly, its asymptotic distribution is a mixed Poisson. We derived the upper bounds for the total variation between the finite and asymptotic distributions. These distributions are illustrated by examples; the related total values are provided in table 1.

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size., CC BY 4.0Correspondence: ieva.meidute-kavaliauskiene@vilniustech.ltFunding: This research received no external funding

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size., CC BY 4.0Correspondence: ieva.meidute-kavaliauskiene@vilniustech.ltFunding: This research received no external funding

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size., CC BY 4.0Correspondence: ieva.meidute-kavaliauskiene@vilniustech.ltFunding: This research received no external funding

Burr XII distribution is widely applicable in reliability and life testing problems in engineering as well as in survival analysis. The concept of weighted and size- biased sampling and length biased  distribution due to importance of this kind of distributions and it's application  in many fields such as medicine, ecology, reliability and human populations. In this paper, length biased Burr XII  distribution is proposed and studied. Different properties of this new distribution are discussed such as the density function and its behaviour , moments, hazard , survival functions and order statistics. The parameters of this new distribution are estimated by maximum likelihood method . The observed information matrix is derived. Finally, we provide a simulation and real data analysis to see how the new model is applicable in practice.

Environmental researchers, as well as epidemiologists, often encounter the problem of determining the probability of exceeding a high threshold of a variable of interest based on observations that are much smaller than the threshold. Moreover, the data available for that task may only be of moderate size. This generic problem is addressed by repeatedly fusing the real data numerous times with synthetic computer-generated samples. The threshold probability of interest is approximated by certain subsequences created by an iterative algorithm that gives precise estimates. The method is illustrated using environmental data including monitoring data of nitrogen dioxide levels in the air

Here we consider a generalized log-transformed version of the Weibull distribution and investigate some of its important properties like expressions for the cumulative distribution function hazard rate function, quantile function, characteristic function, raw moments, incomplete moments, etc. The distribution and moments of order statistics are obtained along with some results on certain structural properties of the distribution. The maximum likelihood estimation of the parameters of the distribution is attempted for both complete and censored data sets and the usefulness of the distribution is illustrated with the help of real-life data sets from biomedical fields.

Recent breakthroughs in microscopy techniques and fluorescence probes enable the recording of mouse embryogenesis at the cellular level for days, easily generating terabyte-level 3D time-lapse data. Since millions of cells are involved, this information-rich data brings a natural demand for an automated tool for its comprehensive analysis. This tool should automatically (1) detect and segment cells at each time point and (2) track cell migration across time. Most existing cell tracking methods cannot scale to the data with such large size and high complexity. For those purposely designed for embryo data analysis, the accuracy is heavily sacrificed. Here, we present a new computational framework for the mouse embryo data analysis with high accuracy and efficiency. Our framework detects and segments cells with a fully probability-principled method, which not only has high statistical power but also helps determine the desired cell territories and increase the segmentation accuracy. With the cells detected at each time point, our framework reconstructs cell traces with a new minimum-cost circulation-based paradigm, CINDA (CIrculation Network-based DataAssociation). Compared with the widely used minimum-cost flow-based methods, CINDA guarantees the global optimal solution with the best-of-known theoretical worst-case complexity and hundreds to thousands of times practical efficiency improvement. Since the information extracted from a single time point is limited, our framework iteratively refines cell detection and segmentation results based on the cell traces which contain more information from other time points. Results show that this dramatically improves the accuracy of cell detection, segmentation, and tracking. To make our work easy to use, we designed a standalone software, MIVAQ (Microscopic Image Visualization, Annotation, and Quantification), with our framework as the backbone and a user-friendly interface. With MIVAQ, users can easily analyze their data and v

In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration. We have derived the best linear unbiased estimator (BLUE) of the scale parameter of the Muth distribution based on order statistics for some known values of the shape parameter.We have further estimated the scale parameter of Muth distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency of the BLUE relative to the usual unbiased estimator has been also evaluated. An illustration describing the performance of U-statistics estimation method when compared with the classical maximum likelihood method is also given.

Extropy is a recent addition to the family of information measures as a complementary dual of Shannon entropy, to measure the uncertainty contained in a probability distribution of a random variable. A probability distribution can be specified either in terms of the distribution function or by the quantile function. In many applied works, there do not have any tractable distribution function but the quantile function exists, where a study on the quantile-based extropy are of importance. The present paper thus focuses on deriving some properties of extropy and its related measures using quantile function. Some ordering relations of quantile-based residual extropy are presented. We also introduce the quantile-based extropy of order statistics and cumulative extropy and studied its properties. Some applications of empirical estimation of quantile-based extropy using simulation and real data analysis are investigated.

Burr XII distribution is widely applicable in reliability and life testing problems in engineering as well as in survival analysis. The concept of weighted and size- biased sampling and length biased  distribution due to importance of this kind of distributions and it's application  in many fields such as medicine, ecology, reliability and human populations. In this paper, length biased Burr XII  distribution is proposed and studied. Different properties of this new distribution are discussed such as the density function and its behaviour , moments, hazard , survival functions and order statistics. The parameters of this new distribution are estimated by maximum likelihood method . The observed information matrix is derived. Finally, we provide a simulation and real data analysis to see how the new model is applicable in practice.

Burr XII distribution is widely applicable in reliability and life testing problems in engineering as well as in survival analysis. The concept of weighted and size- biased sampling and length biased  distribution due to importance of this kind of distributions and it's application  in many fields such as medicine, ecology, reliability and human populations. In this paper, length biased Burr XII  distribution is proposed and studied. Different properties of this new distribution are discussed such as the density function and its behaviour , moments, hazard , survival functions and order statistics. The parameters of this new distribution are estimated by maximum likelihood method . The observed information matrix is derived. Finally, we provide a simulation and real data analysis to see how the new model is applicable in practice.

Recent breakthroughs in microscopy techniques and fluorescence probes enable the recording of mouse embryogenesis at the cellular level for days, easily generating terabyte-level 3D time-lapse data. Since millions of cells are involved, this information-rich data brings a natural demand for an automated tool for its comprehensive analysis. This tool should automatically (1) detect and segment cells at each time point and (2) track cell migration across time. Most existing cell tracking methods cannot scale to the data with such large size and high complexity. For those purposely designed for embryo data analysis, the accuracy is heavily sacrificed. Here, we present a new computational framework for the mouse embryo data analysis with high accuracy and efficiency. Our framework detects and segments cells with a fully probability-principled method, which not only has high statistical power but also helps determine the desired cell territories and increase the segmentation accuracy. With the cells detected at each time point, our framework reconstructs cell traces with a new minimum-cost circulation-based paradigm, CINDA (CIrculation Network-based DataAssociation). Compared with the widely used minimum-cost flow-based methods, CINDA guarantees the global optimal solution with the best-of-known theoretical worst-case complexity and hundreds to thousands of times practical efficiency improvement. Since the information extracted from a single time point is limited, our framework iteratively refines cell detection and segmentation results based on the cell traces which contain more information from other time points. Results show that this dramatically improves the accuracy of cell detection, segmentation, and tracking. To make our work easy to use, we designed a standalone software, MIVAQ (Microscopic Image Visualization, Annotation, and Quantification), with our framework as the backbone and a user-friendly interface. With MIVAQ, users can easily analyze their data and v

Risk measures, such as value-at-risk and expected shortfall, are widely used in finance. With the necessary sample size being computed using asymptotic expansions for relative errors, we propose a general framework to simulate these risk measures for a wide class of dependent data. The asymptotic expansions are new even for independent and identical data. An extensive numerical study is conducted to compare the proposed algorithm against existing algorithms, showing that the new algorithm is easy to implement, fast and accurate, even at the 0.001 quantile level. Applications to the estimation of intra-horizon risk and to a comparison of the relative errors of value-at-risk and expected shortfall are also given. © 2021 Wiley Periodicals LLC

In this article, a new "odds generalized gamma-G" family of distributions, called the GG-G family of distributions, is introduced. We propose a complete mathematical and statistical study of this family, with a special focus on the Fréchet distribution as baseline distribution. In particular, we provide infinite mixture representations of its probability density function and its cumulative distribution function, the expressions for the Rényi entropy, the reliability parameter and the probability density function of ith order statistic. Then, the statistical properties of the family are explored. Model parameters are estimated by the maximum likelihood method. A regression model is also investigated. A simulation study is performed to check the validity of the obtained estimators. Applications on real data sets are also included, with favorable comparisons to existing distributions in terms of goodness-of-fit.

In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent distribution is absolutely continuous (with respect to the Lebesgue measure on the real line). The distribution is identified through the form of the density with respect to a measure which is a sum of the bivariate Lebesgue measure on R2 and the univariate Lebesgue measure on the diagonal {(x, x) : x ∈ R}. We are also interested in the question to what extent conditional expectation of one of such order statistic given another determines the parent distribution. In particular, we provide a new characterization by linearity of regression of an order statistic from the extended sample given the one from the original sample, special case of which solves a problem explicitly stated in the literature. It appears that to describe the correct parent distribution it is convenient to use quantile density functions. In several other cases of regressions of order statistics we provide new results regarding uniqueness of the distribution in the sample. Nevertheless the general question of identifiability of the parent distribution by regression of order statistics from overlapping samples remains open.

In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent distribution is absolutely continuous (with respect to the Lebesgue measure on the real line). The distribution is identified through the form of the density with respect to a measure which is a sum of the bivariate Lebesgue measure on R2 and the univariate Lebesgue measure on the diagonal {(x, x) : x ∈ R}. We are also interested in the question to what extent conditional expectation of one of such order statistic given another determines the parent distribution. In particular, we provide a new characterization by linearity of regression of an order statistic from the extended sample given the one from the original sample, special case of which solves a problem explicitly stated in the literature. It appears that to describe the correct parent distribution it is convenient to use quantile density functions. In several other cases of regressions of order statistics we provide new results regarding uniqueness of the distribution in the sample. Nevertheless the general question of identifiability of the parent distribution by regression of order statistics from overlapping samples remains open.

In this article, we proposed and studied the inverted exponentiated gamma distribution (IEGD). IEGD is obtained by considering the inverse transformation of exponentiated gamma variate. This distribution has been motivated by the extensive use of the exponentiated gamma model in many applied areas and also due to the fact that this new generalization provides more flexibility to analyze real data with upside down bathtub (UBT) hazard rate. The shape of the distribution has been traced mathematically and found that the proposed model is compatible with UBT hazard rate models. The tail area property is also presented based on the idea of Marshall and Olkin (2007) and it is concluded that the new model belongs to the family of heavy-tailed distributions. Some other characteristics such as reliability, hazard, the quantile function, skewness and kurtosis, stochastic ordering, stress-strength reliability and order statistics have been explicitly derived. The classical and Bayesian estimation procedures have been discussed to estimate the unknown parameter of IEGD. The performances of classical and Bayes estimators are studied in terms of average mean square error (MSE) by conducting Monte Carlo simulations. Finally, a real data set with UBT type hazard rate is analyzed for the illustrative purpose of the study.

We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to “large-trimming” properties of extremal processes and a variety of applications. Our point process approach facilitates a connection with the negative binomial process of Gregoire (1984) and consequently to certain generalised versions of the Poisson–Dirichlet distribution.

In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent distribution is absolutely continuous (with respect to the Lebesgue measure on the real line). The distribution is identified through the form of the density with respect to a measure which is a sum of the bivariate Lebesgue measure on R2 and the univariate Lebesgue measure on the diagonal {(x, x) : x ∈ R}. We are also interested in the question to what extent conditional expectation of one of such order statistic given another determines the parent distribution. In particular, we provide a new characterization by linearity of regression of an order statistic from the extended sample given the one from the original sample, special case of which solves a problem explicitly stated in the literature. It appears that to describe the correct parent distribution it is convenient to use quantile density functions. In several other cases of regressions of order statistics we provide new results regarding uniqueness of the distribution in the sample. Nevertheless the general question of identifiability of the parent distribution by regression of order statistics from overlapping samples remains open.

For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.

In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent distribution is absolutely continuous (with respect to the Lebesgue measure on the real line). The distribution is identified through the form of the density with respect to a measure which is a sum of the bivariate Lebesgue measure on R2 and the univariate Lebesgue measure on the diagonal {(x, x) : x ∈ R}. We are also interested in the question to what extent conditional expectation of one of such order statistic given another determines the parent distribution. In particular, we provide a new characterization by linearity of regression of an order statistic from the extended sample given the one from the original sample, special case of which solves a problem explicitly stated in the literature. It appears that to describe the correct parent distribution it is convenient to use quantile density functions. In several other cases of regressions of order statistics we provide new results regarding uniqueness of the distribution in the sample. Nevertheless the general question of identifiability of the parent distribution by regression of order statistics from overlapping samples remains open.

For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.

We introduce a new class of distributions called the Marshall-Olkin generalized-G family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, order statistics are discussed. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.

We examine Peter Hall's early research, undergraduate teaching, and PhD supervision, using the theme of extreme order statistics to highlight interesting aspects of these activities. Focusing on this period allows us to see Peter when, like all academics in the early part of their careers, he was becoming an academic and still establishing himself. That he succeeded so greatly and rapidly began to make the many remarkable contributions that adorn his distinguished career, makes this early, formative stage particularly interesting to explore.

[DE] The safety analysis of nuclear power plant is moving toward a realistic approach in which the simulations performed using best estimate computer codes must be accompanied by an uncertainty analysis, known as the Best Estimate Plus Uncertainties approach. The most popular statistical method used in these analyses is the Wilts' method, which is based on the principle of order statistics for determining a certain coverage of the Figures of-Merit with an appropriate degree of confidence. However, there exist other statistical techniques that could provide similar or even better results. This paper explores the performance of alternative non-parametric methods as compared to the Wilks' method of obtaining such Figure-of-Merits tolerance intervals. Three methods are investigated, i.e. Hutson and Beran-Hall methods and a bootstrap method. All the techniques have been used to perform the uncertainty analysis of a Large-Break Loss of Coolant Accident. The Figure-of-Merit of interest in this application is the maximum value reached by the Peaking Clad Temperature. In order to analyze the results obtained by the different methods, four performance metrics are proposed to measure the coverage, dispersion, conservativeness, and robustness of the tolerance intervals. (C) 2018 Elsevier Ltd. All rights reserved.

For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.

Metaheuristic algorithms are often applied to numerous optimization problems, involving large-scale and mixed-integer instances, specifically. In this contribution we discuss some refinements from the extreme value theory to the lately proposed modification of partition-based random search. The partition-based approach performs iterative random sampling at given feasible subspaces in order to exclude the less favourable regions. The quality of particular regions is evaluated according to the promising index of a region. From statistical perspective, determining the promising index is equivalent to the endpoint estimation of a probability distribution induced by the objective function at the sampling subspace. In the following paper, we give a short review of the recent endpoint estimators derived on the basis of extreme value theory, and compare them by simulations. We discuss also the difficulties in their application and suitability of the estimators for various optimization instances.

[DE] The safety analysis of nuclear power plant is moving toward a realistic approach in which the simulations performed using best estimate computer codes must be accompanied by an uncertainty analysis, known as the Best Estimate Plus Uncertainties approach. The most popular statistical method used in these analyses is the Wilts' method, which is based on the principle of order statistics for determining a certain coverage of the Figures of-Merit with an appropriate degree of confidence. However, there exist other statistical techniques that could provide similar or even better results. This paper explores the performance of alternative non-parametric methods as compared to the Wilks' method of obtaining such Figure-of-Merits tolerance intervals. Three methods are investigated, i.e. Hutson and Beran-Hall methods and a bootstrap method. All the techniques have been used to perform the uncertainty analysis of a Large-Break Loss of Coolant Accident. The Figure-of-Merit of interest in this application is the maximum value reached by the Peaking Clad Temperature. In order to analyze the results obtained by the different methods, four performance metrics are proposed to measure the coverage, dispersion, conservativeness, and robustness of the tolerance intervals. (C) 2018 Elsevier Ltd. All rights reserved.

In this thesis we primarily focus on developing tractable dynamic market models, together with applications of these models. We also address several open questions concerning the statistical properties of static market models. The original research contained in this thesis begins when we define a new distribution, called a general non-central hypergeometric distribution, which models biased sampling without replacement. We then consider a classic mechanism design market model with unit traders in which buyer valuations and seller costs are independent and, on each side of the market, identically distributed. We show that the equilibrium quantity traded has a general non-central hypergeometric distribution under a broad class of mechanisms, where the sampling bias encodes information about the distribution of buyer values relative to seller costs, strategic behaviour of market participants and rent extraction by the market intermediary. We then extend this work by developing a general approach to approximating outcomes in large markets. In particular, we show that the joint distribution of the equilibrium quantity traded and welfare is asymptotically normal, compute the parameters of the approximating normal distribution and bound the approximation rate. We then turn our attention to dynamic market models in which traders with persistent types arrive over time and focus on optimally assessing the tradeoff between the benefits of increasing market thickness and the cost of delay. We start by considering a two-period extension of the classic model of Myerson and Satterthwaite and derive the class of Bayesian optimal mechanisms. Investigating the properties of these mechanisms, we compare them to benchmark static mechanisms and find that dynamics tends to increase the convexity of the region of trade in period one. Motivated by the computational complexity of these optimal mechanisms, we consider approximate implementation in the form of a price-posting mechanism, befor

Tato diplomová práce se zaměřuje na modelování a simulaci nejvyšších pojištěných škod při katastrofách ve světě. Cílem práce je teoreticky popsat metody pravděpodobnostního modelování rizik související s výskytem a ekonomickými důsledky přírodních katastrof a aplikovat je na reálná publikovaná data., This diploma thesis focuses on modeling and simulation of the highest insured damages in the world. The main aim of this thesis is to describe methods of probability modeling of risks related to occurrence and economic consequences of natural disasters and to apply them to real published data., Fakulta ekonomicko-správní, Studentka seznámila komisi s diplomovou prací s názvem Modelování a simulace nejvyšších pojištěných škod při katastrofách ve světě. Studentka zodpověděla následující otázky: Doplňte jednotky u obrázků 4 a 5 (str. 19 a 22). Zaměřte se na výklad a aplikaci metod simulace pomocí kvantilové funkce. Odkud jste brala reálná data, která jste zpracovávala? Jaký ukazatel jste určila z použitých dat? Jakým testem jste ověřovala vhodnost Paretova rozdělení?

This article aims to present the application of probability modelling and simulations based on quantile function of extreme insured losses in the world natural catastrophes based on data in time period 1970-2014, published in Swiss Re Sigma No2/2015. Quantile function provides an appropriate and flexible approach to the probability modelling needed to obtain well-fitted tails. We are specifically interested in modelling and simulations the tails of loss distributions. In a number of applications of quantile functions in insurance and reinsurance risk management interest focuses particularly on the extreme observations in the upper tail of probability distribution. Fortunately it is possible to simulate the observations in one tail of distribution without simulating the central values. This advantage will be used for estimate a few extreme high insured losses in the world's natural catastrophes in future., Tento článek si klade za cíl představit využití pravděpodobnostního modelování a simulací založených na užití kvantilové funkce pro extrémní pojistné události, a to na základě dat ze světových přírodních katastrof v období 1970-2014, která byla zveřejněna v Swiss Re Sigma No2/2015. Kvantilová funkce poskytuje vhodný a pružný přístup k pravděpodobnostnímu modelování a simulacím, které jsou potřebné k získání dobře odhadnutých koncových částí rozdělení. Pozornost je především věnována modelování a simulaci ocasu ztratové distribuční funkce. V řadě aplikací v pojišťovnictví a řízení rizik je kvantilová funkce užívána především na extrémní pozorování v horní části ocasu rozdělení pravděpodobnosti. Naštěstí je možné simulovat pozorování v ocasu distribuční funkce bez simulování centrálních hodnot. Tato výhoda bude použita pro odhad několika extrémně vysokých škod pro pojistné události u světových přírodních katastrof v budoucnu.

Ranked set sampling (RSS) is a sampling approach that can produce improved statistical inference when the ranking process is perfect. While some inferential RSS methods are robust to imperfect rankings, other methods may fail entirely or provide less efficiency. We develop a nonparametric procedure to assess whether the rankings of a given RSS are perfect. We generate pseudo-samples with a known ranking and use them to compare with the ranking of the given RSS sample. This is a general approach that can accommodate any type of raking, including perfect ranking. To generate pseudo-samples, we consider the given sample as the population and generate a perfect RSS. The test statistics can easily be implemented for balanced and unbalanced RSS. The proposed tests are compared using Monte Carlo simulation under different distributions and applied to a real data set.

The current regression models for interval-valued data ignore the extreme nature of the lower and upper bounds of intervals. A new estimation approach is proposed; it considers the bounds of the interval as realizations of the max/min order statistics coming from a sample of nt random draws from the conditional density of an underlying stochastic process {Yt}. This approach is important for data sets for which the relevant information is only available in interval format, e.g., low/high prices. The interest is on the characterization of the latent process as well as in the modeling of the bounds themselves. A dynamic model is estimated for the conditional mean and conditional variance of the latent process, which is assumed to be normally distributed, and for the conditional intensity of the discrete process {nt}, which follows a negative binomial density function. Under these assumptions, together with the densities of order statistics, maximum likelihood estimates of the parameters of the model are obtained. They are needed to estimate the expected value of the bounds of the interval. This approach is implemented with the time series of livestock prices, of which only low/high prices are recorded making the price process itself a latent process. It is found that the proposed model provides an excellent fit of the intervals of low/high returns with an average coverage rate of 83%. In addition, a comparison with current models for interval-valued data is offered.

Here we consider an extended version of the Kumaraswamy modified inverse Weibull distribution and investigate some of its theoretical properties through deriving expressions for cumulative distribution function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, median, mode etc. Certain reliability measures of the distribution are obtained along with the distribution and moments of its order statistics. The maximum likelihood estimation of the parameters of the distribution is discussed and certain real life data applications are given for illustrating the usefulness of the model. Further, with the help of simulated data sets it is shown that the average bias and mean square errors of the maximum likelihood estimators are in decreasing order as the sample size increases.

We consider an ad-hoc network of wireless sensors that harvest energy from the environment and broadcasts measurements independently, at random, provided sufficient energy is available. Clients arriving at the network are interested in retrieving measurements from an arbitrary set of sensors of some fixed size s. We show that the sensors broadcast measurements according to a phase-type distribution. We determine the probability distribution of the time needed for a client to retrieve s sensor measurements. We provide a closed-form expression for the retrieval time of s sensor measurements for an asymptotically large capacity of the sensor battery or the rate at which energy is harvested. We also analyze numerically the retrieval time of s sensor measurements under various assumptions regarding the battery capacity of the sensors, the energy harvesting and consumption processes. The results provide a lower bound for the energy storage capacity of the sensors for which the retrieval time of measurements is below a targeted level. It is also shown that the ratio between the energy harvesting rate and the broadcasting rate significantly influences the retrieval time of measurements, whereas deploying sensors with large batteries does not significantly reduce the retrieval time of measurements. Numerical experiments also indicate that our theoretical results generalize to non-identical energy harvesting rates, various amount of energy consumed upon a broadcast and non-exponential distributions of the energy harvesting and broadcasting processes., Air Transport & Operations