Journal of Data Science

Though, fertility is a biological phenomenon but it depends heavily on socioeconomic, demographic and cultural factors; therefore, this article describes a regression technique to estimate the TFR under dierent proposed model assumptionsand the effects of socioeconomic and demographic factors on TFR as well. The developed methodology also leads to estimate the number of births averted due to the use of family planning methods and percent of increase in births in the absence of birth control devices for 29 states of India using three different methods of births aversion through the National Family Health Survey (NFHS-III) data. The finding shows that there is a variation in number of births averted and percent of increase in births in the absence of family planning methods at the state level in India. The effective use of contraception and maximum number of births avoided due to use of family planning is in Maharashtra and Uttar pradesh. Highest percent of increase in births in the absence of contraception is in Himachal Pradesh and Andhra Pradesh

A new four parameter extreme value distribution is defined and studied. Various structural properties of the proposed distribution including ordinary and incomplete moments, generating functions, residual and reversed residual life functions, order statistics are investigated. Some useful characterizations based on two truncated moments as well as based on the reverse hazard function and on certain functions of the random variable are presented. The maximum likelihood method is used to estimate the model parameters. Further, we propose a new extended regression model based on the logarithm of the new distribution. The new distribution is applied to model three real data sets to prove empirically its flexibility.

This study aims to compare various quantitative models to forecast monthly foreign tourist arrivals (FTAs) to India. The models which are considered here include vector error correction (VEC) model, Naive I and Naive II models, seasonal autoregressive integrated moving average (SARIMA) model and Grey models. A model based on combination of single forecast values using simple average (SA) method has also been applied. The forecasting performance of these models have been compared under mean absolute percentage error (MAPE) and U-statistic (Ustat) criteria. Empirical findings suggest that the combination model gives better forecast of FTAs to India relative to other individual time series models considered here.

In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new models as well as contains two new families as special cases. We explore four special models for the new family. Some mathematical properties of the new family including quantile function, ordinary and incomplete moments, probability weighted moments, Rѐnyi entropy and order statistics are derived. The estimation of the model parameters is performed via maximum likelihood method. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.

A new log location-scale regression model with applications to voltage and Stanford heart transplant data sets is presented and studied. The martingale and modified deviance residuals to detect outliers and evaluate the model assumptions are defined. The new model can be very useful in analysing and modeling real data and provides more better fits than other regression models such as the log odd log-logistic generalized half-normal, the log beta generalized half-normal, the log generalized half-normal, the log-Topp-Leone odd log- logistic-Weibull and the log-Weibull models. Characterizations based on truncated moments as well as in terms of the reverse hazard function are presented. The maximum likelihood method is discussed to estimate the model parameters by means of a graphical Monte Carlo simulation study. The flexibility of the new model illustrated by means of four real data sets.

Forward regression has been criticised heavily and one of the many reasons is regarding its speed and its stopping criteria. The main focus of this paper is on demonstrating how to make it efficient, using R. Our method worksfor continuous predictor variables only, as the use of the partial correlation plays the most important role.

We define and study a three-parameter model with positive real support called the exponentiated generalized extended Pareto distribution. We provide a comprehensive mathematical treatment and prove that the formulas related to the new model are simple and manageable. We study the behaviour of the maximum likelihood estimates for the model parameters using Monte Carlo simulation. We take advantage of applied studies and offer two applications to real data sets that proves empirically the power of adjustment of the new model when compared to another twelve lifetime distributions.

A new class of distributions called the beta linear failure rate power series (BLFRPS) distributions is introduced and discussed. This class of distributions contains new and existing sub-classes of distributions including the beta exponential power series (BEPS) distribution, beta Rayleigh power series (BRPS) distribution, generalized linear failure rate power series (GLFRPS) distribution, generalized Rayleigh power series (GRPS) distribution, generalized exponential power series (GEPS) distribution, Rayleigh power series (RPS) distributions, exponential power series (EPS) distributions, and linear failure rate power series (LFRPS) distribution of Mahmoudi and Jafari (2014). The special cases of the BLFRPS distribution include the beta linear failure rate Poisson (BLFRP) distribution, beta linear failure rate geometric (BLFRG) distribution of Oluyede, Elbatal and Huang (2014), beta linear failure rate binomial (BLFRB) distribution, and beta linear failure rate logarithmic (BLFRL) distribution. The BLFRL distribution is also discussed in details as a special case of the BLFRPS class of distributions. Its structural properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are derived and presented. Maximum likelihood estimation method is used for parameters estimation. Maximum likelihood estimation technique is used for parameter estimation followed by a Monte Carlo simulation study. Application of the model to a real dataset is presented.

We fit a Cox proportional hazards (PH) model to interval-censored survival data by first subdividing each individual's failure interval into nonoverlapping sub-intervals. Using the set of all interval endpoints in the data set, those that fall into the individual's interval are then used as the cut points for the sub-intervals. Each sub-interval has an accompanying weight calculated from a parametric Weibull model based on the current parameter estimates. A weighted PH model is then fit with multiple lines of observations corresponding to the sub-intervals for each individual, where the lower end of each sub-interval is used as the observed failure time with the accompanying weights incorporated. Right-censored observations are handled in the usual manner. We iterate between estimating the baseline Weibull distribution and fitting the weighted PH model until the regression parameters of interest converge. The regression parameter estimates are fixed as an offset when we update the estimates of the Weibull distribution and recalculate the weights. Our approach is similar to Satten et al.'s (1998) method for interval-censored survival analysis that used imputed failure times generated from a parametric model in a PH model. Simulation results demonstrate apparently unbiased parameter estimation for the correctly specified Weibull model and little to no bias for a mis-specified log-logistic model. Breast cosmetic deterioration data and ICU hyperlactemia data are analyzed.

Many software reliability growth models based upon a non-homogeneous Poisson process (NHPP) have been proposed to measure and asses the reliability of a software system quantitatively. Generally, the error detection rate and the fault content function during software testing is considered to be dependent on the elapsed time testing. In this paper we have proposed three software reliability growth models (SRGM’s) incorporating the notion of error generation over the time as an extension of the delayed S-shaped software reliability growth model based on a non-homogeneous Poisson process (NHPP). The model parameters are estimated using the maximum likelihood method for interval domain data and three data sets are provided to illustrate the estimation technique. The proposed model is compared with the existing delayed S-shaped model based on error sum of squares, mean sum of squares, predictive ratio risk and Akaike’s information criteria using three different data sets. We show that the proposed models perform satisfactory better than the existing models.