Incomplete Gamma Distribution: A New Two Parameter Lifetime Distribution with Survival Regression Model

We introduce a new two parameter lifetime distribution constructed via incomplete gamma function which includes exponential distribution as a limiting case. This distribution is more flexible than most of the two parameter extended exponential distributions. Various statistical properties such as moments, moment generating function and certain useful characterizations based on the ratio of two truncated moments are presented. Maximum likelihood estimation method is used for estimating parameters of this distribution and a survival regression model based on the proposed distribution is presented for fitting breast cancer data set

Bias-corrected Maximum-Likelihood Estimator for the Parameter of the Logarithmic Series Distribution and its Characterizations

In this article, we study parameter estimation of the logarithmic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown parameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parameter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numerical results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An example via a real dataset is presented for the illustrative purposes

Optimal Location Design for Prediction of Spatial Correlated Environmental Functional Data

The optimal choice of sites to make spatial prediction is critical for a better understanding of really spatio-temporal data. It is important to obtain the essential spatio-temporal variability of the process in determining optimal design, because these data tend to exhibit both spatial and temporal variability. Two new methods of prediction for spatially correlated functional data are considered. The first method models spatial dependency by fitting variogram to empirical variogram, similar to ordinary kriging (univariate approach). The second method models spatial dependency by linear model co-regionalization (multivariate approach). The variance of prediction method was chosen as the optimization design criterion. An application to CO concentration forecasting was conducted to examine possible differences between the design and the optimal design without considering temporal structure

A New Generalized Modified Weibull Distribution

We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer’s G–function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as evidenced via goodness–of–fit tests

(R1239) A New Type II Half Logistic-G family of Distributions with Properties, Regression Models, System Reliability and Applications

This study proposes a new family of distributions based on the half logistic distribution. With the new family, the baseline distributions gain flexibility through additional shape parameters. The important statistical properties of the proposed family are derived. A new generalization of the Weibull distribution is used to introduce a location-scale regression model for the censored response variable. The utility of the introduced models is demonstrated in survival analysis and estimation of the system reliability. Three data sets are analyzed. According to the empirical results, it is observed that the proposed family gives better results than other existing models

Type II General Exponential Class of Distributions

In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class

Condition monitoring of spar-type floating wind turbine drivetrain using statistical fault diagnosis

Operation and maintenance costs are significant for large‐scale wind turbines and particularly so for offshore. A well‐organized operation and maintenance strategy is vital to ensure the reliability, availability, and cost‐effectiveness of a system. The ability to detect, isolate, estimate, and perform prognoses on component degradation could become essential to reduce unplanned maintenance and downtime. Failures in gearbox components are in focus since they account for a large share of wind turbine downtime. This study considers detection and estimation of wear in the downwind main‐shaft bearing of a 5‐MW spar‐type floating turbine. Using a high‐fidelity gearbox model, we show how the downwind main bearing and nacelle axial accelerations can be used to evaluate the condition of the bearing. The paper shows how relative acceleration can be evaluated using statistical change‐detection methods to perform a reliable estimation of wear of the bearing. It is shown in the paper that the amplitude distribution of the residual accelerations follows a t‐distribution and a change‐detection test is designed for the specific changes we observe when the main bearing becomes worn. The generalized likelihood ratio test is extended to fit the particular distribution encountered in this problem, and closed‐form expressions are derived for shape and scale parameter estimation, which are indicators for wear and extent of wear in the bearing. The results in this paper show how the proposed approach can detect and estimate wear in the bearing according to desired probabilities of detection and false alarm

The Kumaraswamy Weibull Geometric Distribution with Applications

‎In this work‎, ‎we study the kumaraswamy weibull geometric ($Kw-WG$) distribution which includes as special cases‎, ‎several models such as the kumaraswamy weibull distribution‎, ‎kumaraswamy exponential distribution‎, ‎weibull geometric distribution‎, ‎exponential geometric distribution‎, ‎to name a few‎. ‎This distribution was monotone and non-monotone hazard rate functions‎, ‎which are useful in lifetime data analysis and reliability‎. ‎We derive some basic properties of the $Kw-WG$ distribution including noncentral $r$th‎-moments, ‎skewness‎, ‎kurtosis‎, ‎generating functions‎, ‎mean deviations‎, ‎mean residual life‎, ‎entropy‎, ‎order statistics and certain characterizations of our distribution‎. ‎The method of maximum likelihood is used for estimating the model parameters and a simulation study to investigate the behavior of this estimation is presented‎. ‎Finally‎, ‎an application of the new distribution and its comparison with recent flexible generalization of weibull distribution is illustrated via two real data sets‎