In this paper, a new family of distributions, called the Kumaraswamy odd log-logistic, is proposed and studied. Some mathematical properties are presented and special models are discussed. The asymptotes and shapes are investigated. The family density function is given by a linear combination of exponentiated densities following the same baseline model. We derive a power series for the quantile function, explicit expressions for the moments, quantile and generating functions and order statistics. We provide a bivariate extension of the new family. Its performance is illustrated by means of two real data sets.

In this paper, we introduce a new two-parameter distribution which is called new Odd Log-Logistic Half-Logistic (NOLL-HL) distribution. Theoretical properties of this model including the hazard function, survival function, asymptotic, extreme value, quantile function, moments, conditional moments, mean residual life, mean past lifetime, coefficients of skewness and kurtosis, entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustrated the purposes.

Record values, Inter-record times, Statistical evidence, Extreme value distribution, Weibull distribution,

No abstract

Background: Colorectal cancer (CRC) is the third prevalent cancer worldwide, and it includes 10% of all cancer mortality. In Iran, men and women have the third and the fourth incidence rate of CRC, respectively. Survival analysis methods deal with data that measure the time until an event occurs. Artificial neural networks (ANN) and Cox regression are methods for survival analysis. Objectives: The current study was designated to determine related factors to CRC patients' survival using ANN and Cox regression. Methods: In this historical cohort, information of patients who were diagnosed with CRC in Omid Hospital of Mashhad was collected. A total of 157 subjects were investigated from 2006 to 2011 and were followed up until 2016. In ANN, data were divided into two groups of training and testing, and the best neural network architecture was determined based on the area under the ROC curve (AUC). Cox regression model was also fitted and the accuracy of these two models in survival prediction was compared by AUC. Results: The mean and standard deviation of age was 56.4 ± 14.6 years. The three-, five-and seven-year survival rates of patients were 0.67, 0.62, and 0.58, respectively. Using test dataset, the area under curve was estimated 0.759 for the chosen model in ANN and 0.544 for Cox regression model. Conclusions: In this study, ANN is an appropriate approach for predicting CRC patients' survival which was superior to Cox regression. Thus, it is recommended for predicting and also determining the influence of risk factors on patients' survival.