scholarly journals Estimate survival function by using Dagum distribution

2020 ◽  
Vol 1591 ◽  
pp. 012033
Author(s):  
Hind Jawad Kadhim Al-Bderi
Keyword(s):  
Survival Function ◽  
Dagum Distribution

Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

2020 ◽  
Vol 72 (2) ◽  
pp. 111-121
Author(s):  
Abdurakhim Akhmedovich Abdushukurov ◽  
Rustamjon Sobitkhonovich Muradov
Keyword(s):  
Relative Risk ◽  
Sample Size ◽  
Censored Data ◽  
Survival Function ◽  
Survival Functions ◽  
Power Structures ◽  
Bivariate Survival ◽  
Empirical Estimates ◽  
Bivariate Survival Function ◽  
Product Limit

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

scholarly journals A Unified Formulation of k-Means, Fuzzy c-Means and Gaussian Mixture Model by the Kolmogorov–Nagumo Average

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 518
Author(s):  
Osamu Komori ◽  
Shinto Eguchi
Keyword(s):  
Pareto Distribution ◽  
Statistical Data ◽  
Learning Algorithm ◽  
Survival Function ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Simulation Studies ◽  
Probabilistic Framework ◽  
Underlying Distribution ◽  
Fuzzy C Means

Clustering is a major unsupervised learning algorithm and is widely applied in data mining and statistical data analyses. Typical examples include k-means, fuzzy c-means, and Gaussian mixture models, which are categorized into hard, soft, and model-based clusterings, respectively. We propose a new clustering, called Pareto clustering, based on the Kolmogorov–Nagumo average, which is defined by a survival function of the Pareto distribution. The proposed algorithm incorporates all the aforementioned clusterings plus maximum-entropy clustering. We introduce a probabilistic framework for the proposed method, in which the underlying distribution to give consistency is discussed. We build the minorize-maximization algorithm to estimate the parameters in Pareto clustering. We compare the performance with existing methods in simulation studies and in benchmark dataset analyses to demonstrate its highly practical utilities.

scholarly journals The Stability of the Aggregate Loss Distribution

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 91 ◽  
Author(s):  
Riccardo Gatto
Keyword(s):  
Stability Analysis ◽  
Survival Function ◽  
Saddlepoint Approximation ◽  
Computational Formula ◽  
Important Indicator ◽  
The Common ◽  
Infinitesimal Perturbation ◽  
Aggregate Loss ◽  
Aggregate Loss Distribution ◽  
The Stability

In this article we introduce the stability analysis of a compound sum: it consists of computing the standardized variation of the survival function of the sum resulting from an infinitesimal perturbation of the common distribution of the summands. Stability analysis is complementary to the classical sensitivity analysis, which consists of computing the derivative of an important indicator of the model, with respect to a model parameter. We obtain a computational formula for this stability from the saddlepoint approximation. We apply the formula to the compound Poisson insurer loss with gamma individual claim amounts and to the compound geometric loss with Weibull individual claim amounts.

scholarly journals A systematic review of the quality of conduct and reporting of survival analyses of tuberculosis outcomes in Africa

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Moses M. Ngari ◽  
Susanne Schmitz ◽  
Christopher Maronga ◽  
Lazarus K. Mramba ◽  
Michel Vaillant
Keyword(s):  
Systematic Review ◽  
Sample Size ◽  
Survival Function ◽  
Sample Size Estimation ◽  
Size Estimation ◽  
Survival Curves ◽  
Survival Analyses ◽  
Survival Regression

Abstract Background Survival analyses methods (SAMs) are central to analysing time-to-event outcomes. Appropriate application and reporting of such methods are important to ensure correct interpretation of the data. In this study, we systematically review the application and reporting of SAMs in studies of tuberculosis (TB) patients in Africa. It is the first review to assess the application and reporting of SAMs in this context. Methods Systematic review of studies involving TB patients from Africa published between January 2010 and April 2020 in English language. Studies were eligible if they reported use of SAMs. Application and reporting of SAMs were evaluated based on seven author-defined criteria. Results Seventy-six studies were included with patient numbers ranging from 56 to 182,890. Forty-three (57%) studies involved a statistician/epidemiologist. The number of published papers per year applying SAMs increased from two in 2010 to 18 in 2019 (P = 0.004). Sample size estimation was not reported by 67 (88%) studies. A total of 22 (29%) studies did not report summary follow-up time. The survival function was commonly presented using Kaplan-Meier survival curves (n = 51, (67%) studies) and group comparisons were performed using log-rank tests (n = 44, (58%) studies). Sixty seven (91%), 3 (4.1%) and 4 (5.4%) studies reported Cox proportional hazard, competing risk and parametric survival regression models, respectively. A total of 37 (49%) studies had hierarchical clustering, of which 28 (76%) did not adjust for the clustering in the analysis. Reporting was adequate among 4.0, 1.3 and 6.6% studies for sample size estimation, plotting of survival curves and test of survival regression underlying assumptions, respectively. Forty-five (59%), 52 (68%) and 73 (96%) studies adequately reported comparison of survival curves, follow-up time and measures of effect, respectively. Conclusion The quality of reporting survival analyses remains inadequate despite its increasing application. Because similar reporting deficiencies may be common in other diseases in low- and middle-income countries, reporting guidelines, additional training, and more capacity building are needed along with more vigilance by reviewers and journal editors.

scholarly journals p53-dependent and p53-independent activation of apoptosis in mammary epithelial cells reveals a survival function of EGF and insulin.

1995 ◽  
Vol 128 (6) ◽  
pp. 1185-1196 ◽  
Author(s):  
G R Merlo ◽  
F Basolo ◽  
L Fiore ◽  
L Duboc ◽  
N E Hynes
Keyword(s):  
Mammary Epithelial Cells ◽  
P53 Protein ◽  
Survival Function ◽  
Mammary Epithelial ◽  
Nuclear Accumulation ◽  
Temperature Sensitive ◽  
Dna Damaging Agents ◽  
A Cells ◽  
Hc11 Cells ◽  
P53 Tumor Suppressor Protein

The p53 tumor suppressor protein has been implicated as a mediator of programmed cell death (PCD). A series of nontransformed mammary epithelial cell (MEC) lines were used to correlate p53 function with activation of PCD. Treatment of MECs expressing mutant, inactive, or no p53 with DNA-damaging agents did not induce apoptosis. Upon introduction of temperature-sensitive p53 into HC11 cells, which lack wild-type (wt) p53, PCD was observed after mitomycin treatment at 32 degrees, when the ts p53 protein is in wt conformation. Thus, wt p53 mediates activation of PCD in response to mitomycin in HC11 cells. Treatment of the MCF10-A cells, which express wt p53, with various DNA-damaging agents led to nuclear accumulation of p53. Only mitomycin treatment led to an increase in the number of apoptotic nuclei. ErbB-2-transformed MCF10-A cells responded to mitomycin, cisplatin, and 5-Fl-uracil, suggesting that signaling from activated ErbB-2 enhances the cells ability to respond to DNA damage. A combination of high cell density and serum-free medium induces apoptosis in all MECs tested, irrespective of their p53 status. Under these conditions, EGF or insulin act as survival factors in preventing PCD. These data might elucidate some aspects of breast involution and tumorigenesis.

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