Journal of Data Science

The odd inverse Pareto-Weibull distribution is introduced as a new lifetime distribution based on the inverse Pareto and the T-X family. Some mathematical properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is derived. The importance and flexibility of the proposed model are assessed using a real data.

In this paper, parameter estimation for the power Lomax distribution is studied with different methods as maximum likelihood, maximum product spacing, ordinary least squares, weighted least squares, Cramér–von Mises and Bayesian estimation by Markov chain Monte Carlo (MCMC). Robust estimation of the stress-strength model for the Power Lomax distribution is discussed. We propose that the method of maximum product of spacing for reliable estimation of stress-strength model as an alternative method to maximum likelihood and Bayesian estimation methods. A numerical study using real data and Monte Carlo Simulation is performed to compare between different methods.

In this paper we use the maximum likelihood (ML) and the modified maximum likelihood (MML) methods to estimate the unknown parameters of the inverse Weibull (IW) distribution as well as the corresponding approximate confidence intervals. The estimates of the unknown parameters are obtained based on two sampling schemes, namely, simple random sampling (SRS) and ranked set sampling (RSS). Comparison between the different proposed estimators is made through simulation via their mean square errors (MSE), Pitman nearness probability (PN) and confidence length.

We introduce a four-parameter distribution, called the Zografos-Balakrishnan Burr XII distribution. Our purpose is to provide a Burr XII generalization that may be useful to still more complex situations. The new distribution may be an interesting alternative to describe income distributions and can also be applied in actuarial science, finance, bioscience, telecommunications and modelling lifetime data, for example. It contains as special models some well-known distributions, such as the log-logistic, Weibull, Lomax and Burr XII distributions, among others. Some of its structural properties are investigated. The method of maximum likelihood is used for estimating the model parameters and a simulation study is conducted. We provide two application to real data to demonstrate the usefulness of the proposed distribution. Since the Risti´c-Balakrishnan Burr XII distribution has a similar structure to the studied distribution, we also present some of its properties and expansions.

The generalized gamma model has been used in several applied areas such as engineering, economics and survival analysis. We provide an extension of this model called the transmuted generalized gamma distribution, which includes as special cases some lifetime distributions. The proposed density function can be represented as a mixture of generalized gamma densities. Some mathematical properties of the new model such as the moments, generating function, mean deviations and Bonferroni and Lorenz curves are provided. We estimate the model parameters using maximum likelihood. We prove that the proposed distribution can be a competitive model in lifetime applications by means of a real data set.

This article discusses the estimation of the Generalized Power Weibull parameters using the maximum product spacing (MPS) method, the maximum likelihood (ML) method and Bayesian estimation method under squares error for loss function. The estimation is done under progressive type-II censored samples and a comparative study among the three methods is made using Monte Carlo Simulation. Markov chain Monte Carlo (MCMC) method has been employed to compute the Bayes estimators of the Generalized Power Weibull distribution. The optimal censoring scheme has been suggested using two different optimality criteria (mean squared of error, Bias and relative efficiency). A real data is used to study the performance of the estimation process under this optimal scheme in practice for illustrative purposes. Finally, we discuss a method of obtaining the optimal censoring scheme.

Abstract: When comparing the performance of health care providers, it is important that the effect of such factors that have an unwanted effect on the performance indicator (eg. mortality) is ruled out. In register based studies randomization is out of question. We develop a risk adjustment model for hip fracture mortality in Finland by using logistic regression. The model is used to study the impact of the length of the register follow-up period on adjusting the performance indicator for a set of comorbidities. The comorbidities are congestive heart failure, cancer and diabetes. We also introduce an implementation of the minimum description length (MDL) principle for model selection in logistic regression. This is done by using the normalized maximum likelihood (NML) technique. The computational burden becomes too heavy to apply the usual NML criterion and therefore a technique based on the idea of sequentially normalized maximum likelihood (sNML) is introduced. The sNML criterion can be evaluated efficiently also for large models with large amounts of data. The results given by sNML are then compared to the corresponding results given by the traditional AIC and BIC model selection criteria. All three comorbidities have clearly an effect on hip fracture mortality. The results indicate that for congestive heart failure all available medical history should be used, while for cancer it is enough to use only records from half a year before the fracture. For diabetes the choice of time period is not as clear, but using records from three years before the fracture seems to be a reasonable choice.

We propose a new generator of continuous distributions, so called the transmuted generalized odd generalized exponential-G family, which extends the generalized odd generalized exponential-G family introduced by Alizadeh et al. (2017). Some statistical properties of the new family such as; raw and incomplete moments, moment generating function, Lorenz and Bonferroni curves, probability weighted moments, Rényi entropy, stress strength model and order statistics are investigated. The parameters of the new family are estimated by using the method of maximum likelihood. Two real applications are presented to demonstrate the effectiveness of the suggested family.

The Power function distribution is a flexible life time distribution that has applications in finance and economics. It is, also, used to model reliability growth of complex systems or the reliability of repairable systems. A new weighted Power function distribution is proposed using a logarithmic weight function. Statistical properties of the weighted power function distribution are obtained and studied. Location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life are derived. Shape indices such as skewness and kurtosis coefficients and order statistics are obtained. Parametric estimation is performed to obtain estimators for the parameters of the distribution using three different estimation methods; namely: the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution.

Abstract: We introduce a new class of continuous distributions called the Ku maraswamy transmuted-G family which extends the transmuted class defined by Shaw and Buckley (2007). Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.