Analyzing survival data with highly negatively skewed distribution: The Gompertz-sinh family

Kahadawala Cooray; Malwane M.A. Ananda

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Analyzing survival data with highly negatively skewed distribution: The Gompertz-sinh family

机译：使用高度负偏斜分布分析生存数据：Gompertz-sinh系列

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In this article, we explore a new two-parameter family of distribution, which is derived by suitably replacing the exponential term in the Gompertz distribution with a hyperbolic sine term. The resulting new family of distribution is referred to as the Gompertz-sinh distribution, and it possesses a thicker and longer lower tail than the Gompertz family, which is often used to model highly negatively skewed data. Moreover, we introduce a useful generalization of this model by adding a second shape parameter to accommodate a variety of density shapes as well as nondecreasing hazard shapes. The flexibility and better fitness of the new family, as well as its generalization, is demonstrated by providing well-known examples that involve complete, group, and censored data.

机译：在本文中，我们探索了一个新的两参数分布族，该族是通过用双曲正弦项适当替换Gompertz分布中的指数项而得出的。由此产生的新的分布族称为Gompertz-sinh分布，它比Gompertz系列具有更粗，更长的尾巴，后者通常用于建模高度负偏斜的数据。此外，我们通过添加第二个形状参数以适应各种密度形状以及不减小的危险形状，对该模型进行了有益的概括。通过提供涉及完整，分组和审查数据的众所周知的示例，可以证明新家族的灵活性和更好的适用性，以及它的概括性。

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来源
《Journal of applied statistics》 |2010年第2期|1-11|共11页
作者
Kahadawala Cooray; Malwane M.A. Ananda;
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作者单位

Department of Mathematics, Central Michigan University, Mount Pleasant, MI, USA;

Department of Mathematical Sciences, University of Nevada, Las Vegas, NV, USA;

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原文格式 PDF
正文语种 eng
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关键词
goodness-of-fit; gompertz distribution; maximum likelihood;

机译：拟合优度Gompertz分布;最大似然;

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机译：伽玛分布的新概括，适用于负偏斜的生存数据
2. The GIGG-EnKF: ensemble Kalman filtering for highly skewed non-negative uncertainty distributions [J] . Bishop Craig H. Quarterly Journal of the Royal Meteorological Society . 2016,第696aPta1期

机译：GIGG-EnKF：集合卡尔曼滤波，用于高度偏斜的非负不确定性分布
3. The GIGG-EnKF: ensemble Kalman filtering for highly skewed non-negative uncertainty distributions [J] . Bishop Craig H. Quarterly Journal of the Royal Meteorological Society . 2016,第696aPta1期

机译：gigg-enkf：Ensemble Kalman滤波对于高度偏斜的非负不确定性分布
4. A hybrid distribution for highly right skewed data [C] . Nehla Debbabi, Marie Kratz, Sadok El Asmi International Conference on Communications and Networking . 2015

机译：高度偏斜数据的混合分布
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6. Cooperation is less likely to evolve in a finite population with a highly skewed distribution of family size [O] . Sabin Lessard 2007

机译：在家庭规模分布高度不对称的有限人群中合作发展的可能性较小
7. Decision-making is the process of analyzing information about a problem situation and comparing it to a specific conclusion in order to solve a specific problematic (Yıkılmaz, 2001; Miller and Byrnes, 2001). Decision-making styles are a mechanism that is influenced by the internal and external conditions that determine the direction of the decisions of the individual, the content of the decision-making process, and the outcome of the decision-making process (Payne, Bettman and Johson, 1993; Bavol’ár and Orosová, 2015). ACT is a contemporary member of the Cognitive Behavioral Therapy family. ACT (Acceptance and commitment therapy) has both similar and different directions with Behavioral Therapies and Cognitive Therapies (Herbet and Forman, 2011; Hayes, 2004). KKT responds to classical behavioral treatments using both existential and cognitive approaches in the analysis of behavior. KKT is a science wing that tries to solve human problems with a wider perspective aimed at solving problematic human behaviors (Plumb, Stewart, Dahl and Lundgren, 2009). It is seen that there is very little research about the new approach of ACT approach when the aiming country of our country is screened and it is thought that our country will contribute to the field of psychological counseling with the work done. In the scope of the research, experimental and control groups and preliminary test, post-test and follow-up measurements of 2x3 experimental design were used. The study's study group consists of a total of 24 (12 experimental and 12 control groups) university students studying in different departments and levels, continuing their education in the academic year of 2015-2016 in Ağrı province and İbrahim Chechen University in 2015-2016 academic year. The average age of participants in the experiment and control group is 20. There were 12 participants in the experimental group, 7 female and 5 male, and 12 participants, 7 female and 5 male in the control group. Personal Information Form and Decision Making Style Scale prepared by the researcher were used in the research. In order to decide on the tests to be used in the course of analyzing the data, the scores of the participant's Decision Styles Scale pre-test, which are placed primarily in the experimental and control groups, it was analyzed whether the basic expectations of parametric tests were answered. As a result of the analysis made, the scores, skewness and kurtosis coefficients obtained from the Decision Making Styles Scale were given to the experimental and control groups. It was determined that the distribution was normal in the result of Shapiro-Wilk test, in which the skewness and kurtosis coefficients of each sub-scale were ranked between -1 and +1. Participants in the experimental and control groups; homogeneity test results for decision-style pre-test measurements indicate that the data are homogeneous. According to the results of the Mauchly Globalness Test, it has been determined that working supports the hypothesis. It was determined that there was no significant difference between the pre-test scores obtained from dependent decision-making style of experiment and control groups, but the test group showed lower mean scores at the significant level within the scores of post-test and follow-up tests. Therefore, it can be said that the ACT-oriented psychoeducation program applied to the experimental group reduces the dependent decision-making style scores from the decision style sub-dimensions and the psychoeducation program has a lasting effect. It was determined that there was no significant difference between pre-test, post-test and follow-up scores obtained from the Spontaneous-Instant Decision Style of experiment and control groups. Thus, it can be said that this situation does not cause a significant difference in the Spontaneous-Decision-Making Style scores from the decision style sub-dimensions of the ACT-oriented psychoeducation program applied to the experimental group. The ACT -oriented psychoeducation program had a decline in the intuitive decision-making styles of the individuals, but this decrease did not create significant differences. Thus, it can be said that this situation does not make a meaningful difference in the intuitive decision style scores from the decision style sub-dimensions of the KKT oriented psychoeducation program applied to the experimental group. The pre-test scores obtained from the rational decision-making style of the experimental and control groups showed that there was a difference between the post-test and the follow-up scores, but this difference was not significant. As a result of the analysis, it was determined that the test group had higher levels of rational decision style than the pre - test scores in the post test and follow - up scores, whereas the post test and follow - up test scores in the control group rational decision style showed a decrease compared to the pre - test scores. the pre - test scores. Decision-making Styles Scale Avoidant Decision Making As a result of the analysis of the mean scores of the subscale scores of pre-test, post-test and follow-up measures, the group effect was found to be insignificant. It was determined that the experimental and control groups differed significantly from the pre-test scores obtained from the avoidant decision-making style but did not show any significant change within the scores of the post-test and follow-up tests. [O] . mustafa ercengiz, ali haydar şar 2018

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8. ESTIMATING PARAMETERS,TESTING FIT,AND ANALYZING UNTRANSFORMED DATA PERTAINING TO THE NEGATIVE BINOMIAL AND OTHER DISTRIBUTIONS. [R] . gurland,john hinz,paul 1970

机译：估计参数，测试结果，并分析负面二项和其他分布的未经传输的数据。

Analyzing survival data with highly negatively skewed distribution: The Gompertz-sinh family

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