Application of Odd Lomax log-logistic distribution to cancer data.

The effectiveness of the parental distribution is modified in this article by adding flexibility, allowing it to capture all characteristics of the provided real-world data sets. This is accomplished by using the T-X class of distributions to generalize the parental distribution. Odd Lomax log-logistic distribution or OLLLD in short, is the name of the generalized parental distribution. The fundamental statistical properties of OLLLD are explicitly expressed. The maximum likelihood estimation approach is used to estimate the unidentified OLLLD parameters. In order to investigate the fit of the approach employed in estimating the parameters of OLLLD, the data are generated and an investigation done. Again, the ability of OLLLD is evaluated by fitting it to the real survival time data set of breast cancer.

Dealing with missing data under stratified sampling designs where strata are study domains.

A quick count seeks to estimate the voting trends of an election and communicate them to the population on the evening of the same day of the election. In quick counts, the sampling is based on a stratified design of polling stations. Voting information is gathered gradually, often with no guarantee of obtaining the complete sample or even information in all the strata. However, accurate interval estimates with partial information must be obtained. Furthermore, this becomes more challenging if the strata are additionally study domains. To produce partial estimates, two strategies are proposed: (1) a Bayesian model using a dynamic post-stratification strategy and a single imputation process defined after a thorough analysis of historic voting information; additionally, a credibility level correction is included to solve the underestimation of the variance and (2) a frequentist alternative that combines standard multiple imputation ideas with classic sampling techniques to obtain estimates under a missing information framework. Both solutions are illustrated and compared using information from the 2021 quick count. The aim was to estimate the composition of the Chamber of Deputies in Mexico.

Semiparametric zero-inflated Bernoulli regression with applications.

When the observed proportion of zeros in a data set consisting of binary outcome data is larger than expected under a regular logistic regression model, it is frequently suggested to use a zero-inflated Bernoulli (ZIB) regression model. A spline-based ZIB regression model is proposed to describe the potentially nonlinear effect of a continuous covariate. A spline is used to approximate the unknown smooth function. Under the smoothness condition, the spline estimator of the unknown smooth function is uniformly consistent, and the regression parameter estimators are asymptotically normally distributed. We propose an easily implemented and consistent estimation method for the variances of the regression parameter estimators. Extensive simulations are conducted to investigate the finite-sample performance of the proposed method. A real-life data set is used to illustrate the practical use of the proposed methodology. The real-life data analysis indicates that the prediction performance of the proposed semiparametric ZIB regression model is better compared to the parametric ZIB regression model.

Testing for correlation between two time series using a parametric bootstrap.

We study the problem of determining if two time series are correlated in the mean and variance. Several test statistics, originally designed for determining the correlation between two mean processes or goodness-of-fit testing, are explored and formally introduced for determining cross-correlation in variance. Simulations demonstrate the theoretical asymptotic distribution can be ineffective in finite samples. Parametric bootstrapping is shown to be an effective tool in such an enterprise. A large simulation study is provided demonstrating the efficacy of the bootstrapping method. Lastly, an empirical example explores a correlation between the Standard & Poor's 500 index and the Euro/US dollar exchange rate while also demonstrating a level of robustness for the proposed method.

Process capability indices in normal distribution with the presence of outliers.

Process capability indices (PCIs) are useful measures to evaluate the performance and capability of a process when it is under control. Assuming the specification variable is distributed from a normal population, several PCIs are derived by the researchers. Also, many scientists have worked on these indices when data are contaminated with outliers as well as in the homogenous case. But, in almost all studies, they evaluated the effect of outliers on the PCIs nonparametrical and used robust methods. Here, the parametric model of outliers is considered and introduced the PCIs based on the outliers model. Therefore, these indices are estimated based on the maximum-likelihood and moment estimator of the unknown parameters of the normal distribution contaminated by outliers. Finally, the performances of these measures as well as their parametric and nonparametric estimators are discussed by using simulation studies and several numerical examples. It has been seen that parametric estimation has better performances than a nonparametric method.

Inference of progressively type-II censored competing risks data from Chen distribution with an application.

In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation-maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes.

Out-of-Sample Fusion in Risk Prediction.

The probability that mortality from certain causes exceeds high thresholds is addressed. An out-of-sample fusion method is presented where an original real data sample is fused or combined with independent computer-generated samples in the estimation of exceedance probabilities assuming a density ratio model. Since the size of the combined sample of real and artificial data is larger than that of the real sample, the fused sample produces short confidence intervals relative to traditional methods. Numerical results show that the method maintains good coverage even for some misspecified cases.