On transform orders for largest claim amounts

This paper investigates the ordering properties of largest claim amounts in heterogeneous insurance portfolios in the sense of some transform orders, including the convex transform order and the star order. It is shown that the largest claim amount from a set of independent and heterogeneous exponential claims is more skewed than that from a set of independent and homogeneous exponential claims in the sense of the convex transform order. As a result, a lower bound for the coefficient of variation of the largest claim amount is established without any restrictions on the parameters of the distributions of claim severities. Furthermore, sufficient conditions are presented to compare the skewness of the largest claim amounts from two sets of independent multiple-outlier scaled claims according to the star order. Some comparison results are also developed for the multiple-outlier proportional hazard rates claims. Numerical examples are presented to illustrate these theoretical results.

New estimations of child marriage: Evidence from 98 low- and middle-income countries

The Sustainable Development Goals include a target on eliminating child marriage, a human rights abuse. Yet, the indicator used in the SDG framework is a summary statistic and does not provide a full picture of the incidence of marriage at different ages. This paper aims to address this limitation by providing an alternative method of measuring child marriage. The paper reviews recent data on nuptiality and captures evidence of changes in the proportion married and in the age at marriage, in 98 low- and middle-income countries (LMICs). Using data collected from nationally representative Demographic and Health Surveys and Multiple Indicator Cluster Surveys, survival analysis is applied to estimate (a) age-specific marriage hazard rates among girls before age 18; and (b) the number of girls that were married before age 18 in 2020. Results show that the vast majority of girls remain unmarried until age 10. Child marriage rates increase gradually until age 14 and accelerate significantly thereafter at ages 15–17. By accounting for both single-year-age-specific child marriage hazard rates and the age structure of the population with a survival analysis approach, lower estimates in countries with a rapid decrease in child marriage and higher estimates in countries with constant or slightly rising child marriage rates relative to the direct approach are obtained.

Identifying Influential Prognostic Factors of Death Hazard Rates in Patients with Chronic Kidney Disease (CKD) Using Weibull Model with Non-Constant Shape Parameter

Introduction: Chronic Kidney Disease (CKD) is a disease in which damaged kidneys could not remove waste material from the blood which could result in other health problems. The aim of this analysis was to identify significant laboratory prognostic factors on death hazard due to CKD. Methods: There were 109 patients with end-stage renal disease (ESRD) treated at Helal pharmaceutical and clinical complex. The survival time was set as the time interval from starting dialysis until death due to CKD. Age, gender and factors such as creatinine, cholesterol, uric acid, SGOT, SGPT, bilirubin, hemoglobin, potassium, ALP, HbA1C, ferritin, calcium, phosphorus, PTH and albumin were employed in this study. Weibull Distribution with non-Constant Shape Parameter versus constant Shape Parameter for the analysis were used. Results: Death due to CKD occurred in 29 (26.6%) of the patients. Sixty-seven (61.5%) had uric acid higher than 6.8 (mg/dl) and 39(35%) had phosphorus higher than 4.7 (mg/dl) which were poor prognoses. The incidence of death was 48.4%. Calcium<8.5 (mg/dl) (p=0.002), Calcium > 9.5 (mg/dl) (p=0.003), Albumin 4-6.3 (g/dl) (p=0.034), Phosphorus (p=0.022), hemoglobin<10 (g/dl) (p=0.043), hemoglobin>12.5 (g/dl) (p=0.006) and iPTH (p<0.001) were significant variables which had an effect on death hazard rates. Conclusion: The Weibull model with Non-Constant shape parameter was suggested to be more accurate for identifying risk factors, leading to more precise results, compared to constant shape parameter. Investigators mostly emphasize on the importance of Calcium, Albumin, Phosphorus, hemoglobin and iPTH for reducing hazard rates in CKD patients.

Further Results on the Proportional Vitalities Model

In contrast to many survival models such as proportional hazard rates and proportional mean residual lives, the proportional vitalities model has also been introduced in the literature. In this paper, further stochastic ordering properties of a dynamic version of the model with a random vitality growth parameter are investigated. Examples are presented to illustrate different established properties of the model. Potentials for inference about the parameters in proportional vitalities model with possibly time-varying effects are also argued and discussed.

The four-parameter exponentiated Weibull model with Copula, properties and real data modeling.

A new four-parameter lifetime model is introduced and studied. The new model derives its flexibility and wide applicability from the well-known exponentiated Weibull model. Many bivariate and the multivariate type versions are derived using the Morgenstern family and Clayton copula. The new density can exhibit many important shapes with different skewness and kurtosis which can be unimodal and bimodal. The new hazard rate can be decreasing, J-shape, U-shape, constant, increasing, upside down and increasing-constant hazard rates. Various of its structural mathematical properties are derived. Graphical simulations are used in assessing the performance of the estimation method. We proved empirically the importance and flexibility of the new model in modeling various types of data such as failure times, remission times, survival times and strengths data.

Small High-Risk Uveal Melanomas Have a Lower Mortality Rate

Our aim was to determine whether size impacts on the difference in metastatic mortality of genetically high-risk (monosomy 3) uveal melanomas (UM). We undertook a retrospective analysis of data from a patient cohort with genetically characterized UM. All patients treated for UM in the Liverpool Ocular Oncology Centre between 2007 and 2014, who had a prognostic genetic tumor analysis. Patients were subdivided into those with small (≤2.5 mm thickness) and large (>2.5 mm thickness) tumors. Survival analyses were performed using Gray rank statistics to calculate absolute probabilities of dying as a result of metastatic UM. The 5-year absolute risk of metastatic mortality of those with small monosomy 3 UM was significantly lower (23%) compared to the larger tumor group (50%) (p = 0.003). Small disomy 3 UM also had a lower absolute risk of metastatic mortality (0.8%) than large disomy 3 UM (6.4%) (p = 0.007). Hazard rates showed similar differences even with lead time bias correction estimates. We therefore conclude that earlier treatment of all small UM, particularly monosomy 3 UM, reduces the risk of metastatic disease and death. Our results would support molecular studies of even small UM, rather than ‘watch-and-wait strategies’.

Comparisons of Parallel Systems with Components Having Proportional Reversed Hazard Rates and Starting Devices

In this paper, we consider stochastic comparisons of parallel systems with proportional reversed hazard rate (PRHR) distributed components equipped with starting devices. By considering parallel systems with two components that PRHR and starting devices, we prove the hazard rate and reversed hazard rate orders. These results are then generalized for such parallel systems with n components in terms of usual stochastic order. The establish results are illustrated with some examples.

Clarifying the mediation dilemma: A response to “Sticks and carrots for peace”

This brief essay considers the “mediation dilemma” in the light of new analysis by Constantin Ruhe and Iris Volg. Ruhe and Volg’s analysis adds to our understanding of manipulative mediation in two important ways: (a) it demonstrates how an analysis that uses a lens of survival functions clarifies the policy trade-offs beyond what is possible from an analysis that uses a lens of changing hazard rates; and (b) it demonstrates that lighter (nonmanipulative) forms of mediation have a less positive effect on peace stability than in the original analysis. This response also offers important corrections to the conclusions drawn by Ruhe and Volg: (a) ignoring the lens of changing hazard rates misses key ways of testing for the observable implications that arise from the underlying theoretical arguments; (b) Ruhe and Volg misstate some of the theoretical claims made by Beardsley; and (c) almost all of the original implications explored by Beardsley remain supported.

The Theoretical Overview of Generalized Gumbel Type-Ⅱ Distribution

A new version of weighted model is introduced by assigning weights to Gumbel Distribution Type Ⅱ (GDT-Ⅱ) to make it more useful and flexible in life time data .This paper provides an understanding of some basic statistical properties of (WGDT-Ⅱ).It includes moments and maximum likelihood estimator. In addition to the above it imparts the insight to distribution function, survival rate, hazard rate and reverse hazard rate. The behavior of PDF, CDF, and Survival rate, Hazard rates and Reverse Hazard rates has been presented through various graphs by setting different values of parameters.