Construction of <i>k</i>-Variate Survival Functions with Emphasis on the Case <i>k</i>= 3

The purpose of this paper is to present a general universal formula for k-variate survival functions for arbitrary k = 2, 3, ..., given all the univariate marginal survival functions. This universal form of k-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case k = 2 and the main results for the case k = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general k ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the k = 3 and k ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the k-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the copula methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.

Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

The reliability of power transformers is subject to service age and health condition.This paper proposes a practical model for the evaluation of two reliability indices:survival function(SF)and mean residual life(MRL).In the proposed model,the periodical modeling of power transformers are considered for collecting the information on health conditions.The corresponding health condition is assumed to follow a continuous semi-Markov process for representing a state transition.The proportional hazard model(PHM)is introduced to incorporate service age and health condition into hazard rate.In addition,the proposed model derives the analytical formulas for and offers the analytical evaluation of SF and MRL.SF and MRL are calculated for new components and old components,respectively.In both cases,the proposed model offers rational results which are compared with those obtained from comparative models.The results obtained by the contrast of the proposed analytical method and the Monte Carlo method.The impact of differentmodel parameters and the coefficient of variation(CV)on reliability indices are discussed in the case studies.

Prediction Method Study on the Remaining Useful Life of Plant New Varieties Rights Based on Weibull Survival Function and Gaussian Model——Taking Hybrid Rice Variety for Example

In view of the difficulty in determining remaining useful life of plant new variety right in economic analysis, Weibull Survival Analysis Method and Gaussian Model to were used to study how to accurately estimate the remaining useful life of plant new variety right. The results showed that the average life of the granted rice varieties was 10.013 years. With the increase of the age of plant variety rights, the probability of the same residual life Ttreaching x was smaller and smaller, the reliability lower and lower, while the probability of the variety rights becoming invalid became greater. The remaining useful life of a specific granted rice variety was closely related to the demonstration promotion age when the granted rice variety reached its maximum area and the appearance of alternative varieties, and when the demonstration promotion age of the granted rice variety reaching the one with the maximum area, the promotion area would be decreased once a new alternative variety appeared, correspondingly with the shortening of the remaining useful life of the variety. Therefore, Weibull Survival Analysis Method and Gaussian Model could describe the remaining useful life＇s time trend, as well as determine the remaining useful life of a concrete plant variety right, clarify the entire life time of varieties rights, and make the economic analysis of plant new varieties rights more accurate and reasonable.

Cox Proportional Hazard Model for Survival Time of Neonatal Mortality in Neonatal Intensive Care Unit of Hospitals in River Nile State-Sudan

Cox Proportional Hazard model is a popular statistical technique for exploring the relationship between the survival time of neonates and several explanatory variables. It provides an estimate of the study variables’ effect on survival after adjustment for other explanatory variables, and allows us to estimate the hazard (or risk) of death of newborn in NICU of hospitals in River Nile State-Sudan for the period (2018-2020). Study Data represented (neonate gender, mode of delivery, birth type, neonate weight, resident type, gestational age, and survival time). Kaplan-Meier method is used to estimate survival and hazard function for survival times of newborns that have not completed their first month. Of 700 neonates in the study area, 25% of them died during 2018-2020. Variables of interest that had a significant effect on neonatal death by Cox Proportional Hazard Model analysis were neonate weight, resident type, and gestational age. In Cox Proportional Hazard Model analysis all the variables of interest had an effect on neonatal death, but the variables with a significant effect included, weight of neonate, resident type and gestational age.

Log-Rank Test for Comparing Survival Curves of Neonatal Mortality Characteristic Groups in River Nile State-Sudan

This paper concerns the Log-rank test for comparing survival curves of neonatal mortality characteristic groups in River Nile State, Sudan. In this paper, log-rank test is used to compare two or more survival curves for the characteristics of newborn associated with newborn death after using Kaplan-Meier methods to estimate and graph survival curves for the variable of interest as (sex of newborn, weight of newborn, gestational age, mode of delivery and resident type), at the hospital of River Nile state—Sudan, with a sample size 700 of newborn in which the admission to the Neonatal Intensive Care Unit (NICU) of those hospitals during the period 2018-2020. In term of risk of death for newborn we found that 25% of sample study for newborns who were born in River Nile State-Sudan died. In addition, we conclude that after the log-rank statistics and Kaplan-Meier methods were applied, gender does not affect the newborn’s risk of survival, while the risk of survival increases when the birth weight is greater than 4.35 kg and the gestational age is greater than 42 weeks. There is no difference in the probability of survival for newborns whether the delivery is normal or cesarean. However, newborns are significantly more likely to survive in urban areas than in rural areas.

A comparative study of pancreatic endocrine function and related metabolism after long-term survival between the patients with combined kidneypancreas transplantation vs those with combined en bloc ' liver-pancreas transplantation

Objective To compare the effects of combined en bloc liver - pancreas transplantation ( LPT) with portal vein drainage and simultaneous combined kidney - pancreas transplantation ( KPT) with systemic venous drainage on the pancreatic endocrine function and related me-

The NBEE and NWEE classes of lifetime distributions and their properties

A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of lifetime X and its equilibrium Xo. The relationships of the NBEE （NWEE） and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate （IFR）, new better than used （NBU） and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE （NWEE） lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE（NWEE） if and only if the corresponding discrete failure distribution belongs to the discrete NBEE（NWEE）. While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.

The Cox Proportional Hazard Regression Model Vis-à-Vis ITN-Factor Impact on Mortality Due to Malaria

This study has provided a starting point for defining and working with Cox models in respect of multivariate modeling. In medical researches, there may be situations, where several risk factors potentially affect patient prognosis, howbeit, only one or two might predict patient’s predicament. In seeking to find out which of the risk factors contribute the most to the survival times of patients, there was the need for researchers to adjust the covariates to realize their impact on survival times of patients. Aside the multivariate nature of the covariates, some covariates might be categorical while others might be quantitative. Again, there might be cases where researchers need a model that has the capability of extending survival analysis methods to assessing simultaneously the effect of several risk factors on survival times. This study unveiled the Cox model as a robust technique which could accomplish the aforementioned cases. An investigation meant to evaluate the ITN-factor vis-à-vis its contribution towards death due to Malaria was exemplified with the Cox model. Data were taken from hospitals in Ghana. In doing so, we assessed hospital in-patients who reported cases of malaria (origin state) to time until death or censoring (destination stage) as a result of predictive factors (exposure to the malaria parasites) and some socioeconomic variables. We purposefully used Cox models to quantify the effect of the ITN-factor in the presence of other risk factors to obtain some measures of effect that could describe the relationship between the exposure variable and time until death adjusting for other variables. PH assumption holds for all three covariates. Sex of patient was insignificant to deaths due to malaria. Age of patient and user status were both significant. The magnitude of the coefficient (0.384) of ITN user status depicts its high contribution to the variation in the dependent variable.

On the Application of Nadarajah Haghighi Gompertz Distribution as a Life Time Distribution

The convolution of Nadarajah-Haghighi-G family of distributions will result into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) than each of them individually in terms of the estimate of the characteristics in there parameters. The combination was done using Nadarajah-Haghighi (NH) generator. We investigated in the newly developed distribution some basic properties including moment, moment generating function, survival rate function, hazard rate function asymptotic behaviour and estimation of parameters. The proposed model is much more flexible and has a better representation of data than Gompertz distribution and some other model considered. A real data set was used to illustrate the applicability of the new model.

Effects of combined radiation and thermal burn injury on the survival of skin allograft and immune function in rats

Abstract Objectives To investigate the effects of combined radiation and thermal burn injury on the survival of skin allografts and to analyze the relationship between the prolongation of allograft survival and the changes of immune functions of the thymocytes and splenocytes in rats. Methods Wistar rats were irradiated with 3, 4, 5, 6 and 8 Gy of gamma rays. Thirty minutes after radiation, 15% TBSA Ⅲ degree burn was inflicted to the rats. Twenty four hours after the burn injury, allografts were used to cover the burn wounds. In the 8 Gy group, 1 hour before skin grafting, the bone marrow cells (4×10 8) from the same donor were also transplanted. All rats were carefully observed after injury. The rats with single radiation injury of 5 Gy gamma rays, with single burn injury and with combined radiation burn injury were killed 3, 7, 10, 15 and 30 days after skin grafting for immunological assay and pathological study. Results All the allografts in the single burn group were rejected in 10 days. In the combined injury groups, the survival rates of the allografts in rats undergoing 3 and 4 Gy radiation were 20% and 30%, respectively. In the combined injury groups undergoing 5, 6 and 8 Gy radiation, the 10 day survival rates of the allografts were 69%, 88% and 100% respectively, and the 30 day survival rates in the three groups were 36%, 42% and 100% separately. The grafted allogenic skin, with normal epithelial cells and good vascularity, healed well with the recipient's skin. Hairs grew well from the allografts 30 days after grafting. Three, 7 and 15 days after allografting, in the single burn group, the proliferative activities of the thymocytes were 90%, 185% and 130% of the preinjury level, and the antibody forming capacities of the splenocytes were 200%, 171% and 300% of the preinjury level, respectively; in the combined injury groups, the proliferative activities were 6%, 99% and 91% of the preinjury level, and the forming capacities were 2%, 36% and 90% of the preinjury level. Conclusions The survival rate of allograft in rats undergoing combined radiation and thermal burn injury rises with the increase in radiation dosage. The allograft covering single bun injury is severely rejected by immune reaction. The prolongation of the survival of allograft in combined injury group mainly results from radiation that suppresses immune functions.

Random weighting estimation for survival function under right censorship

The random weighting method is an emerging computing method in statistics.In this paper,we propose a novel estimation of the survival function for right censored data based on the random weighting method.Under some regularity conditions,we prove the strong consistency of this estimation.

Asymptotic Normality of the Empirical Distribution under Negatively Associated Sequences and its Applications

By the well-known large and small blocks parting method for dependent situations, we establish the asymptotic normality of the Empirical Distribution Function under Negatively Associated Sequences. As its application in reliablity problems, a natural estimate Fn（x） for the survival function F（x） = P（X 〉 x） is proposed, and the asymptotic normality of n^1/2 [Fn（x） - F（x）] is established.

Imprecise Probability Method with the Power-Normal Model for Accelerated Life Testing

We present a new nonparametric predictive inference(NPI)method using a power-normal model for accelerated life testing(ALT).Combined with the accelerating link function and imprecise probability theory,the proposed method is a feasible way to predict the life of the product using ALT failure data.To validate the method,we run a series of simulations and conduct accelerated life tests with real products.The NPI lower and upper survival functions show the robustness of our method for life prediction.This is a continuous research,and some progresses have been made by updating the link function between different stress levels.We also explain how to renew and apply our model.Moreover,discussions have been made about the performance.

STATISTICAL INFERENCE OF WEIBULL DISTRIBUTION FOR TAMPERED FAILURE RATE MODEL IN PROGRESSIVE STRESS ACCELERATED LIFE TESTING

In this note,the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time.For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull,maximum likelihood estimation is investigated.

Statistical inference for right-censored data with nonignorable missing censoring indicators

We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be consistent and converges to a Gaussian process. Furthermore, we develop an empirical processbased testing method to check the MAR (missing at random) mechanism, and establish asymptotic properties for the proposed test statistic. To determine the critical value of the test, a consistent model-based bootstrap method is suggested. We conduct simulation studies to evaluate the numerical performance of the proposed method and compare it with existing methods. We also analyze a real data set from a breast cancer study for an illustration.

On Renyi entropies of order statistics

In this paper we consider a generalize dynamic entropy measure and prove that this mea- sure characterizes the distribution function uniquely. Also we propose cumulative resi- dual R^nyi entropy of order statistics and prove that it also determines the distribution function uniquely. Applications of entropy concepts to DNA sequence analysis, the ulti- mate support for the biological systems, have been widely explored by researchers. The entropy measures discussed here can be applied for analysis of ordered DNA sequences.