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The geometric process has been widely studied in various disciplines and applied in reliability, maintenance and warranty cost analysis, among others. In its applications in maintenance policy optimisation, the geometric process assumes constant repair effectiveness by its process rate. Nevertheless, in practice, maintenance effectiveness may differ from time to time and can therefore be better depicted by a random variable. Motivated by this argument, this paper proposes a new variant of the geometric process, which is referred to as the rate randomized geometric process (RRGP). The probabilistic properties of the RRGP are then investigated. The maximum likelihood method is utilised to estimate the parameters of the RRGP. Numerical examples are given to show its applicability in both maintenance policy optimization and fitting real‐world failure datasets. [ABSTRACT FROM AUTHOR]

Abstract This research commences a unit statistical model named power new power function distribution, exhibiting a thorough analysis of its complementary properties. We investigate the advantages of the new model, and some fundamental distributional properties are derived. The study aims to improve insight and application by presenting quantitative and qualitative perceptions. To estimate the three unknown parameters of the model, we carefully examine various methods: the maximum likelihood, least squares, weighted least squares, Anderson–Darling, and Cramér-von Mises. Through a Monte Carlo simulation experiment, we quantitatively evaluate the effectiveness of these estimation methods, extending a robust evaluation framework. A unique part of this research lies in developing a novel regressive analysis based on the proposed distribution. The application of this analysis reveals new viewpoints and improves the benefit of the model in practical situations. As the emphasis of the study is primarily on practical applications, the viability of the proposed model is assessed through the analysis of real datasets sourced from diverse fields.

In this article, we unravel an extension of shifted version of Lindley distribution, termed as extended generalized shifted Lindley (EGSL) distribution. Stochastic ordering, moment generating function, reliability characteristics and other relevant properties are studied for this distribution. To estimate the parameters involved, method of maximum likelihood is performed. A detailed simulation study for several choices of parameters is executed as well. Finally, as a comparative exploration, possible fitting of the proposed distribution to a real data along with model fitting by other competent distributions is documented through the aid of a few model checking criteria.

This research commences a unit statistical model named power new power function distribution, exhibiting a thorough analysis of its complementary properties. We investigate the advantages of the new model, and some fundamental distributional properties are derived. The study aims to improve insight and application by presenting quantitative and qualitative perceptions. To estimate the three unknown parameters of the model, we carefully examine various methods: the maximum likelihood, least squares, weighted least squares, Anderson–Darling, and Cramér-von Mises. Through a Monte Carlo simulation experiment, we quantitatively evaluate the effectiveness of these estimation methods, extending a robust evaluation framework. A unique part of this research lies in developing a novel regressive analysis based on the proposed distribution. The application of this analysis reveals new viewpoints and improves the benefit of the model in practical situations. As the emphasis of the study is primarily on practical applications, the viability of the proposed model is assessed through the analysis of real datasets sourced from diverse fields. [ABSTRACT FROM AUTHOR]

We prove existence and uniqueness for the inverse-first-passage time problem for soft-killed Brownian motion using rather elementary methods relying on basic results from probability theory only. We completely avoid the relation to a suitable partial differential equation via a suitable Feynman–Kac representation, which was previously one of the main tools. [ABSTRACT FROM AUTHOR]

Accelerated degradation tests (ADTs) are widely used to assess lifetime information under normal use conditions for highly reliable products. For the accelerated tests, two basic assumptions are that changing stress levels does not affect the underlying distribution family and that there is stochastic ordering for the life distributions at different stress levels. The acceleration invariance (AI) principle for ADTs is proposed to study these fundamental assumptions. Using the AI principle, a theoretical connection between the model parameters and the accelerating variables is developed for Hougaard processes. This concept can be extended to heterogeneous gamma and inverse Gaussian processes. Simulation studies are presented to support the applicability and flexibility of the Hougaard process using the AI principle for ADTs. A real data analysis using the derived relationship is used to validate the AI principle for accelerated degradation analysis. All technical details, simulation results for nonlinear cases and model mis‐specification analysis are available online as Supporting Information. [ABSTRACT FROM AUTHOR]

We propose a class of cure rate models motivated by analysis of colon cancer and triple-negative breast cancer survival data. This class is indexed by an adaptive activation parameter and a function. We establish that the class is stochastically ordered in the activation parameter and also establish two identifiability results for this class. The first- and last-activation models are members of this class whereas many cure rate models proposed in the literature are also part of this class. We illustrate that while first- and last-activation models may perform poorly under model misspecifications, the proposed model with adaptive activation provides appropriate inference in these cases. We apply the proposed approach to assess treatment-sex interaction on cure rate in a colon cancer study and to assess role of tumor heterogeneity and ethnic disparity in breast cancer. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new non-parametric test for testing mean time to failure order. The asymptotic properties of the proposed test statistic are studied. We also develop a jackknife empirical likelihood (JEL) ratio test for testing the mean time to failure order. Using the Monte Carlo simulation study, we establish that the JEL ratio test has good power under various alternatives. Finally, we illustrate the proposed test procedure using two real data sets. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new three-parameter odd log-logistic power inverse Lindley distribution and discuss some of its properties. These include the shapes of the density and hazard rate functions, mixture representation, the moments, the quantile function, and order statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Three algorithms are proposed for generating random data from the proposed distribution. A simulation study is carried out to examine the bias and root mean square error of the maximum likelihood estimators of the parameters. An application of the model to three real data sets is finally presented and compared with the fit attained by some other well-known two and three-parameter distributions for illustrative purposes. It is observed that the proposed model has some advantages in analyzing lifetime data as compared to other popular models in the sense that it exhibits varying shapes and shows more flexibility than many currently available distributions. [ABSTRACT FROM AUTHOR]

The use of truncated exponential distribution (TED) in lifetime experiments was introduced by Hannon and Dahiya (1999), however, the hazard function of TED only describes the increasing failure rate which possesses an asymptotic climb at the truncation point. However, there are so many real-life situations where the behaviour of the hazard function is decreasing. To address this weakness and increase its flexibility, we propose an extension of the TED by adding one more shape parameter and the new generalized distribution is called exponentiated truncated exponential distribution (ETED). The shape behaviour of the new proposed distribution with its failure rate is discussed. Also, moment generating function, mean, median and mode are obtained with stochastic ordering. Two real-world datasets are taken into consideration to demonstrate the relevance and importance of the suggested model (ETED). It is proven that the recommended distribution performs quite well in comparison to exponential, truncated exponential gamma, Weibull, lognormal, and other comparable well-known distributions when used to assess lifetime data. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a brand new extension of the inverse Lomax distribution for fitting engineering time data. The newly developed distribution, termed the transmuted Topp–Leone inverse Lomax (TTLILo) distribution, is characterized by an additional shape and transmuted parameters. It is critical to notice that the skewness, kurtosis, and tail weights of the distribution are strongly influenced by these additional characteristics of the extra parameters. The TTLILo model is capable of producing right-skewed, J-shaped, uni-modal, and reversed-J-shaped densities. The proposed model's statistical characteristics, including the moments, entropy values, stochastic ordering, stress-strength model, incomplete moments, and quantile function, are examined. Moreover, characterization based on two truncated moments is offered. Using Bayesian and non-Bayesian estimating techniques, we estimate the distribution parameters of the suggested distribution. The bootstrap procedure, approximation, and Bayesian credibility are the three forms of confidence intervals that have been created. A simulation study is used to assess the efficiency of the estimated parameters. The TTLILo model is then put to the test by being applied to actual engineering datasets, demonstrating that it offers a good match when compared to alternative models. Two applications based on real engineering datasets are taken into consideration: one on the failure times of airplane air conditioning systems and the other on the active repair times of airborne communication transceivers. Also, we consider the problem of estimating the stress-strength parameter R = P (Z 2 < Z 1) with engineering application. [ABSTRACT FROM AUTHOR]

In this paper, a new continuous distribution with one parameter named weighted Arz distribution (WAD) is suggested using the idea of weighted distributions. Several properties of this distribution such as moments, moment generating function, skewness, coefficient of variation, kurtosis, and index of dispersion are investigated. Also, the distribution of order statistics, Lorenz and Bonferroni curves, Gini index, stochastic ordering, R'enyi entropy, mean deviations about mean and median are provided. The reliability functions including survival, hazard, odds, reversed hazard rate, and mean residual life are provided with supported graphical representation. The maximum likelihood estimate (MLE) of the distribution parameter is provided. A simulation study is conducted to show the consistency of the MLE. Application to COVID-19 data set is presented and showed that the proposed distribution is more flexible than some other competing distributions in fitting such data. [ABSTRACT FROM AUTHOR]

This paper investigates stochastic comparisons of largest claim amounts of two sets of independent or interdependent portfolios in the sense of some stochastic orders. Let random variable Xi$$ {X}_i $$ (i=1,...,n$$ i=1,\dots, n $$) with distribution function F(x;αi)$$ F\left(x;{\alpha}_i\right) $$, represents the claim amount for ith risk of a portfolio. Here two largest claim amounts are compared considering that the claim variables follow a general semiparametric family of distributions having the property that the survival function F‾(x;α)$$ \overline{F}\left(x;\alpha \right) $$ is increasing in α$$ \alpha $$ or is increasing and convex/concave in α$$ \alpha $$. The results obtained in this paper apply to a large class of well‐known distributions including the family of exponentiated/generalized distributions (e.g., exponentiated exponential, Weibull, gamma and Pareto family), Rayleigh distribution and Marshall–Olkin family of distributions. As a direct consequence of some main theorems, we also obtained the results for scale family of distributions. Several numerical examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, a convenient and parsimonious family of the quantile functions is proposed for modeling time-to-event data. Detailed mathematical arguments are presented for deriving the explicit expressions of the quantile density, quantile hazard and quantile mean remaining life functions. Their functional properties are also explored. Some important members of the family are provided. A special case, the so-called additive power logarithmic quantile family, is discussed with detailed properties, parameter estimation and application to time-to-event data. Measures of skewness and kurtosis for the proposed quantile function are derived. Important statistical measures useful for reliability analysis are also provided with their explicit expressions. Stochastic ordering, tail weight and order statistics are also discussed. L-moments are explicitly derived for the proposed quantile function. Estimation is approached using the likelihood function and percentiles. A real data set consists of times between occurrence of the coal-mining accidents is analyzed for illustration purposes. [ABSTRACT FROM AUTHOR]

The study focuses on the development of a new probability distribution with applications to extreme values. The distribution is proposed by incorporating an additional parameter into the inverse Pareto distribution using the α-Power Transformation. Various properties of the new distribution are derived. The paper also explores the estimation of the parameters by the Maximum Likelihood Estimation (MLE) technique. Simulations are performed to evaluate the performance of the MLEs. In addition, two real data sets with extreme values are used to evaluate the efficacy of the proposed model. It is concluded that the proposed model performs well in the case of extreme values compared to the existing distributions.

In this paper, a new Kumaraswamy generalized family is proposed. Four sub-models of the proposed family accommodate symmetrical, left-skewed, bimodal, right-skewed unimodal, and reverse-J densities, as well as increasing, modified bathtub, decreasing, bathtub, upside down bathtub, reverse J and J shaped hazard rates. Its fundamental properties are derived. The maximum likelihood method and seven other methods are used for estimating the model parameters. Numerical simulations are performed to explore the performance of these estimation methods. Three real-life data sets from medicine, agriculture and engineering are fitted to illustrate the flexibility of the proposed family. The proposed family is a good alternative to the Kumaraswamy-G, beta-G, and Topp-Leone-G families. [ABSTRACT FROM AUTHOR]

This paper introduces a new distribution called the power exponentiated Weibull distribution by generalizing the Weibull distribution using the power exponentiated family of distributions. The statistical aspects of the proposed distribution such as the probability density function, cumulative distribution function, and reliability measures are studied. The mixture representation of the distribution is studied. The distribution includes the alpha power Weibull distribution and the power exponentiated exponential distribution as special cases. Statistical properties such as moments, stress strength reliability, Renyi entropy, quantiles, income inequality measures, stochastic ordering, order statistics, etc., are derived. The parameter values of the distribution are obtained using the maximum likelihood estimation method. The maximum likelihood estimates have been inferred by the Monte Carlo simulation study on the proposed distribution, and the adequacy of the proposed distribution is shown by modeling it on real-life cancer-related datasets. The measures such as Akaike information criteria, Bayesian information criteria, Hannan–Quinn information criterion, Anderson–Darling statistic, k-s statistic, p-value, etc., shows that the proposed distribution can provide a better fit compared to the exponentiated power Weibull distribution, the exponentiated exponential distribution, the alpha power Weibull distribution, the Weibull distribution and the exponential distribution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the tampered random variable (TRV) modeling in multiple step-stress life testing experiments. Here τ 1 < τ 2 < ... < τ k − 1 be (k − 1) prespecified time points and s 1 , s 2 , ... , s k be k prefixed stress levels with si being the stress level in force during the time interval [ τ i − 1 , τ i) for i = 1 , ... , k with τ 0 = 0 and τ k = ∞. We define the tampered random variable T TRV (k) in multiple step-stress scenario and calculate the PDF, CDF, and Hazard rate for the proposed tampered variable T TRV (k) . We derive a general expression for the expectation of T TRV (k) under different number k of stress levels and also obtain some results on stochastic ordering for different k. All these results are obtained under arbitrary baseline (under normal stress condition with stress level s1) life distribution. In particular, we consider exponential distribution with mean θ and Weibull distribution with scale parameter λ and shape parameter α for specific expressions. We also prove some results on equivalence of the TRV modeling with the two other existing models for step-stress life testing, namely, cumulative exposure and tampered failure rate. Finally, we consider some variations of the modeling approach for T TRV (k) to include incorporation of the stress levels, discrete life time, bivariate or multivariate life times. [ABSTRACT FROM AUTHOR]

The framework of differential privacy protects an individual’s privacy while publishing query responses on congregated data. In this work, a new noise addition mechanism for differential privacy is introduced where the noise added is sampled from a hybrid density that resembles Laplace in the centre and Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this density has the best characteristics of both distributions. We theoretically analyze the proposed mechanism, and we derive the necessary and sufficient condition in one dimension and a sufficient condition in high dimensions for the mechanism to guarantee $(\epsilon,\delta)$ -differential privacy. Numerical simulations corroborate the efficacy of the proposed mechanism compared to other existing mechanisms in achieving a better trade-off between privacy and accuracy. [ABSTRACT FROM AUTHOR]

The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp–Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp–Leone (TPITL) distribution. The power inverted Topp–Leone and the inverted Topp–Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp–Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.

Lindley distribution is a lifetime model with application in survival analysis and reliability theory problems often centred around its increasing hazard rate function and flexibility over exponential distribution. In this paper, we introduce a new generalization of the Lindley distribution referred to as Lindley Truncated Negative binomial (LTNB) distribution. The LTNB model has increasing, decreasing and upside-down bathtub(UBT) shapes for the hazard rate function. Various properties of the LTNB distribution are studied including moments, quantiles, and stochastic ordering. Characterizations of the new distribution are obtained. Maximum likelihood, Cramer-von-Mises, ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the model parameters. A simulation study is carried out to assess and compare the performance of different estimates. An autoregressive time series model with the LTNB as marginal is developed. The model is fitted to bladder cancer data set to show how the proposed model works in practice. [ABSTRACT FROM AUTHOR]

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson–Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators. [ABSTRACT FROM AUTHOR]

We establish some identities in law for the convolution of a beta prime distribution with itself, involving the square root of beta distributions. The proof of these identities relies on transformations on generalized hypergeometric series obtained via Appell series of the first kind and Thomae's relationships for {}_3F_2(1). Using a self-decomposability argument, the identities are applied to derive complete monotonicity properties for quotients of confluent hypergeometric functions having a doubling character. By means of probability, we also obtain a simple proof of Turán's inequality for the parabolic cylinder function and the confluent hypergeometric function of the second kind. The case of Mill's ratio is discussed in detail. [ABSTRACT FROM AUTHOR]

The current paper presented new two-parameter life processes distribution, the Marshall-Olkin Pranav (MOEP) distribution. This study combines the Marshall-Olkin method with the Pranav distribution to produce a more accessible and flexible model for data survival techniques. Some of its critical statistical features are presented in this study. For instance, we mentioned its survival, hazard, reversed hazard, and cumulative hazard rate function. Then we discussed its Moment generating functions, The characteristic function, Incomplete moments, Rènyi and Entropies, and stochastic orderings. The research utilized maximization of chance in estimating parameters. These tests are done through simulations to achieve the desired results. With an assurance that the combined model has larger applications, such as in the strength of airplane glass and survival data set, the two real-world examples are given to explain the great possibility and validity of the extended distribution. These results demonstrate the usefulness of the proposed distribution and the need for more tilt parameters. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a brand new extension of the inverse Lomax distribution for fitting engineering time data. The newly developed distribution, termed the transmuted Topp–Leone inverse Lomax (TTLILo) distribution, is characterized by an additional shape and transmuted parameters. It is critical to notice that the skewness, kurtosis, and tail weights of the distribution are strongly influenced by these additional characteristics of the extra parameters. The TTLILo model is capable of producing right-skewed, J-shaped, uni-modal, and reversed-J-shaped densities. The proposed model’s statistical characteristics, including the moments, entropy values, stochastic ordering, stress-strength model, incomplete moments, and quantile function, are examined. Moreover, characterization based on two truncated moments is offered. Using Bayesian and non-Bayesian estimating techniques, we estimate the distribution parameters of the suggested distribution. The bootstrap procedure, approximation, and Bayesian credibility are the three forms of confidence intervals that have been created. A simulation study is used to assess the efficiency of the estimated parameters. The TTLILo model is then put to the test by being applied to actual engineering datasets, demonstrating that it offers a good match when compared to alternative models. Two applications based on real engineering datasets are taken into consideration: one on the failure times of airplane air conditioning systems and the other on the active repair times of airborne communication transceivers. Also, we consider the problem of estimating the stress-strength parameter R=P(Z2

The modern trend in distribution theory is to propose hybrid generators and generalized families using existing algebraic generators along with some trigonometric functions to offer unique, more flexible, more efficient, and highly productive G-distributions to deal with new data sets emerging in different fields of applied research. This article aims to originate an odd sine generator of distributions and construct a new G-family called "The Odd Lomax Trigonometric Generalized Family of Distributions". The new densities, useful functions, and significant characteristics are thoroughly determined. Several specific models are also presented, along with graphical analysis and detailed description. A new distribution, "The Lomax cosecant Weibull" (LocscW), is studied in detail. The versatility, robustness, and competency of the LocscW model are confirmed by applications on hydrological and survival data sets. The skewness and kurtosis present in this model are explained using modern graphical methods, while the estimation and statistical inference are explored using many estimation approaches.

The information based on entropy of uncertainty associated with the residual life of a random variable is implemented in various fields, e.g., information theory, statistical physics, reliability theory, statistics, demography and economics, etc. In this paper, we propose two new R ˜ -norm dynamic survival entropy (RNDSE) and R ˜ -norm weighted dynamic survival entropy (RNWDSE) based on the survival function and some results on stochastic ordering are studied in detail. Further, we have investigated the bounds on RNDSE and RNWDSE in terms of failure rate function. In addition, some relationships between RNDSE, RNWDSE and failure function have also been well established. Finally, in order to illustrate the applications of RNDSE and RNWDSE, some useful distributions like exponential, Rayleigh, Weibull, Pareto, finite range distributions and one new distribution called T-exponential have been characterized. [ABSTRACT FROM AUTHOR]

We propose nonparametric tests for testing mean residual life and mean past life ordering. Asymptotic properties of the proposed test statistics are studied. We also propose Jackknife Empirical Likelihood (JEL) ratio tests for testing mean residual life and mean past life ordering. Some numerical results are presented to evaluate the performance of the proposed tests by comparing them with few competing tests available in the literature. Finally, we illustrate the proposed test procedures using real data sets. [ABSTRACT FROM AUTHOR]

In the present work, we study the information generating (IG) function of record values and examine some main properties of it. We establish some comparison results associated with the IG measure of record values. We show that under equality of two given IG measures of upper record values, the corresponding parent distributions can be determined uniquely. We also present some bounds for the IG measure of upper record values based on upper records of a standard exponential distribution. Further, we provide some results associated with characterization of exponential distribution by maximization (minimization) of IG function of record values under some conditions. We also examine the relative information generating (RIG) measure between the distribution of records values and the corresponding underlying distribution and present some results in this regard. To illustrate the results, several examples have been presented through the paper. [ABSTRACT FROM AUTHOR]

Traditionally, in reliability acceptance sampling plans, the decision to accept or reject a lot is made by performing the life tests of items. However, when the item's deterioration is described by a degradation process, it can be made based on the observed deterioration levels of the items obtained from degradation tests. In this paper, two acceptance sampling plans are developed, based on the observation of the deterioration of the items, accumulated on a given period of time. To model the degradation of the items over time, the Wiener process with positive drift is employed. Algorithms to find the parameters of the proposed sampling plans are suggested. Conditionally on the acceptance in the test, the developed sampling plans are shown to improve the reliability performance of the items in the sense that the lifetimes of the items after the reliability sampling test are stochastically larger than those before the test. Also, we compare the two sampling plans both from a technical and economical points of view. [ABSTRACT FROM AUTHOR]

In this paper, by considering two multi-state semi-coherent systems sharing some components, we define the multi-state joint signature. Then, some properties of this multi-state joint signature are discussed in detail, and some preservation results are established in terms of stochastic ordering. A south-east shift order for comparing the multi-state joint signature matrices is then discussed. Finally, some numerical examples are presented for illustrating all the theoretical results established here. [ABSTRACT FROM AUTHOR]

This paper studies stochastic ordering under nonlinear expectations εG generated by solutions of G-Backward Stochastic Differential Equations (G-BSDEs) defined on G-expectation spaces. We derive sufficient conditions for the convex, increasing convex, and monotonic G-stochastic orderings of G-diffusion processes at terminal time. Our approach relies on comparison properties for G-Forward-Backward Stochastic Differential Equations (G-FBSDEs) and on relevant extensions of convexity, monotonicity and continuous dependence properties for the solutions of associated Hamilton-Jacobi-Bellman (HJB) equations. Applications of G-stochastic ordering to contingent claim superhedging price comparison under ambiguous coeffcients are provided. [ABSTRACT FROM AUTHOR]

In this paper, the general proportional mean past lifetime frailty model is considered, from which the unconditional cumulative distribution and density functions of the lifetime variable are derived. Dependency between the two variables are studied. Stochastic comparisons are made through which it is shown that some well-known stochastic orderings between two frailty variables carry over to the corresponding lifetime variables. The effects of baseline variable and the frailty variable on the proposed frailty model are studied. The relative mean past lifetime ordering is introduced and some relative ordering between two lifetime random variables with different frailty variables are studied. Also a simulation study is given to illustrate some results. [ABSTRACT FROM AUTHOR]

To make informed health policy decisions regarding a treatment, we must consider both its cost and its clinical effectiveness. In past work, we introduced the net benefit separation (NBS) as a novel measure of cost‐effectiveness. The NBS is a probabilistic measure that characterizes the extent to which a treated patient will be more likely to experience benefit as compared to an untreated patient. Due to variation in treatment response across patients, uncovering factors that influence cost‐effectiveness can assist policy makers in population‐level decisions regarding resource allocation. In this paper, we introduce a regression framework for NBS in order to estimate covariate‐specific NBS and find determinants of variation in NBS. Our approach is able to accommodate informative cost censoring through inverse probability weighting techniques, and addresses confounding through a semiparametric standardization procedure. Through simulations, we show that NBS regression performs well in a variety of common scenarios. We apply our proposed regression procedure to a realistic simulated data set as an illustration of how our approach could be used to investigate the association between cancer stage, comorbidities and cost‐effectiveness when comparing adjuvant radiation therapy and chemotherapy in post‐hysterectomy endometrial cancer patients. [ABSTRACT FROM AUTHOR]

The site percolation threshold of the hexagonal lattice satisfies 0.656 246 < p c < 0.739 695. For comparison, the largest previous lower bound of 0.652 703… was established in 1981, and the smallest previous upper bound of 0.743 359 was derived in 2007. The bound is obtained by using the substitution method to compare the hexagonal lattice site model to an exactly-solved two-parameter site percolation model on the martini lattice. Computational reductions involving graph-welding, symmetry, non-crossing partitions, and network flow computations overcome challenges to establishing stochastic ordering between the models. [ABSTRACT FROM AUTHOR]

In In this paper power weighted Akash distribution (PWAD) which includes weighted Akash distribution (WAD), power Akash distribution (PAD) and Akash distribution as particular cases has been proposed and investigated. Its moments, hazard rate function and mean residual life function have been discussed. Method of maximum likelihood estimation has been discussed for estimating the parameters of the distribution. Applications of the proposed distribution to two real lifetime datasets have been presented and compared with other one parameter, two-parameter and three-parameter well-known lifetime distributions. [ABSTRACT FROM AUTHOR]

In this paper, a new distribution namely the length biased new quasi-Lindley distribution is proposed with the different weight function. The different mathematical and statistical properties of the proposed distribution are derived and discussed. The survival function, hazard rate function and mean residual life function for the length biased new quasi Lindley distribution is discussed. Also, concepts like stochastic ordering and entropy for proposed distribution are studied. The parameters of the proposed distribution are estimated by using the method of maximum likelihood estimation. The performance of the newly introduced distribution is studied using a real- life data set. [ABSTRACT FROM AUTHOR]

We revisit the classical Schmitter problem in ruin theory and consider it for randomly chosen initial surplus level U. We show that the computational simplification that is obtained for exponentially distributed U allows to connect the problem to m-convex ordering, from which simple and sharp analytical bounds for the ruin probability are obtained, both for the original (but randomized) problem and for extensions involving higher moments. In addition, we show that the solution to the classical problem with deterministic initial surplus level can conveniently be approximated via Erlang(k)-distributed U for sufficiently large k, utilizing the computational advantages of the advocated randomization approach. [ABSTRACT FROM AUTHOR]