International Journal of Statistics and Probability
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Culturally, there is always pressure among newly-wed to conceive early and have births in India. Previous studies have documented relationship between age at first birth & fertility, besides the socio-demographic factors that influence age at first birth. The current study aims answering directions and quantum of such relationships using frailty models. The successive rounds of NFHS data (1, 2, 3 & 4) from Uttar Pradesh is used in the study. Fertility in India is characterized as too-early-too-fast. By age-30 majority women would have completed the childbearing. However, the data from NFHS-4 shows some striking changes in the initiation of child bearing in Uttar Pradesh breaking away from the stereotypes of too early too fast characterization. While 44.67 percent of the women aged 30-34 had experienced first birth by age 18 in the year 1992-93 (NFHS-1), the percentages declined during 2015-16 (NFHS-4) to 28.25%. However, by ages 26 majority of women (>95%) aged 30-34 have had experienced first birth. Births at younger age are also a reflection on enforcement of child-marriage restraint act & adherence to legal minimum age at marriage which is 18 for girls & 21 for boys. The data from NFHS-4 have some quality issues. Women aged as low as 5 have shown to have experienced first birth by that age. This may not be possible. The Kaplan Meier survival Graph provided the survival probabilities with respect of each predictor sub groups. The log rank test was used to test the equality of survivor function for each sub group of the predictor variable. The survivor function was significantly different among sub groups of the predictor variables except for the categories of ever use of contraception at NFHS1 and categories of religion across rounds of NFHS data. The Cox Proportional Hazards model was used to study the risk of first birth by socio demographic characteristics. The Frailty model capturing the unobserved heterogeneity in the event time was preferred over standard survival model. For the current study, gamma frailty with Weibull-hazard is used as it fits the data well. Age at marriage and women’s literacy significantly determines the Age at First Birth. The inverse relationship with regard to ever use of contraception needs further analysis. The model also predicts significant frailty with variance parameter (theta) greater than one across the NFHS datasets.

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 1

The shape parameter estimation using the minimum-variance linear estimator with hyperparameter (MVLE-H) method is believed to be effective for a wear-out failure period in a small sample. In the process of the estimation, our method uses the hyperparameter and estimate shape parameters of the MVLE-H method. To obtain the optimal hyperparameter c, it takes a long time, even in the case of the small sample. The main purpose of this paper is to remove the restriction of small samples. We observed that if we set the shape parameters, for sample size n and c, we can use the regression equation to infer the optimal c from n. So we searched in five increments and complemented the hyperparameter for the remaining sample sizes with a linear regression line. We used Monte Carlo simulations (MCSs) to determine the optimal hyperparameter for various sample sizes and shape parameters of the MVLE-H method. Intrinsically, we showed that the MVLE-H method performs well by determining the hyperparameter. Further, we showed that the location and scale parameter estimations are improved using the shape parameter estimated by the MVLE-H method. We verified the validity of the MVLE-H method using MCSs and a numerical example.

We derive explicit asymptotic confidence intervals for any Markov chain Monte Carlo (MCMC) algorithm with finite asymptotic variance, started at any initial state, without requiring a Central Limit Theorem nor reversibility nor geometric ergodicity nor any bias bound. We also derive explicit non-asymptotic confidence intervals assuming bounds on the bias or first moment, or alternatively that the chain starts in stationarity. We relate those non-asymptotic bounds to properties of MCMC bias, and show that polynomially ergodicity implies certain bias bounds. We also apply our results to several numerical examples. It is our hope that these results will provide simple and useful tools for estimating errors of MCMC algorithms when CLTs are not available.

This study examines design preference in Completely Randomized (CR) split-plot experiments involving random whole plot factor effect and fixed sub-plot factor effect. Many previous works on optimally designing split-plot experiments assumed only factors with fixed levels. However, the cases where interests are on random factors have received little attention. These problems have similarities with optimal design of experiments for fixed parameters of non-linear models because the solution rely on the unknown parameters.  Design Space (DS) containing exhaustive list of balanced designs for a fixed sample size were compared for optimality using the product of determinants of derived information matrices of the Maximum Likelihood (ML) estimators equivalent to random and fixed effect in the model. Different magnitudes of components of variance configurations where variances of factor effects are larger than variances of error term were empirically used for the comparisons. The results revealed that the D-optimal designs are those with whole plot factor levels greater than replicates within each level of whole plot.

In this paper, a new four-parameter extended inverse Weibull distribution called Alpha power Extended Inverse Weibull Poisson distribution is introduced using the alpha power Poisson generator. This method adds two shape parameters to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of Alpha power extended inverse Weibull distribution and the corresponding confidence intervals are obtained. The simulation method is carried out to evaluate the performance of the maximum likelihood estimate in terms of their Absolute Bias and Mean Square Error using simulated data. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to Inverse Weibull distribution, Alpha Power Poisson inverse exponential distribution, Alpha Power Extended Inverse Weibull distribution, and Alpha Power Extended Inverse Exponential distribution.

Handling flood quantile with little data is essential in managing water resources. In this paper, we propose a potential model called Modified Group Method of Data Handling (MGMDH) to predict the flood quantile at ungauged sites in Malaysia. In this proposed MGMDH model, the principal component analysis (PCA) method is matched to the group method of data handling (GMDH) with various transfer functions. The MGMDH model consists of four transfer functions: polynomial, sigmoid, radial basis function, and hyperbolic tangent sigmoid transfer functions. The prediction performance of MGMDH models is compared to the conventional GMDH model. The appropriateness and effectiveness of the proposed models are demonstrated with a simulation study. Cauchy distribution is used in the simulation study as a disturbance error. The implementation of Cauchy Distribution as an error disturbance in artificial data illustrates the performance of the proposed models if the extreme value or extreme event occurs in the data set. The simulation study may say that the MGMDH model is superior to other comparison models, namely LR, NLR, GMDH and ANN models. Another beauty of this proposed model is that it shows a strong prediction performance when multicollinearity is absent in the data set.

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 10, No. 6, 2021

Despite global efforts in alleviating poverty, many people are still living in poverty. Different methods were employed to estimate poverty with many researchers moving from monetary to multidimensional poverty modeling approach. In Namibia, very few studies have been conducted to estimate poverty in a multidimensional sense. The 2015/2016 Namibia household income and expenditure survey dataset was employed to develop multidimensional poverty indices (MPIs) using beta distribution. We showed that the MPI is equivalent to the mean of the left truncated beta distribution. The results revealed that the northern regions of Namibia are the most affected by multidimensional poverty. The results from this study can be used to identify areas that are severely affected by poverty and consequently form a basis to develop appropriate measures intended to alleviate poverty.

In this article, additional properties of the Gumbel-Burr XII distribution, denoted by (GBXII(L)), defined in (Osatohanmwen et al., 2017), are studied. We consider some useful characterizations for the GBXII(L) distribution and some of its properties. A simulation study is conducted to assess the performance of the MLEs and the usefulness of the GBXII(L) distribution is illustrated by means of three real data sets. The simulation study suggests that the maximum likelihood method can be used to estimate the distribution parameters, and the three examples show that the GBXII(L) is very flexible in fitting different shapes of data. A log-GBXII(L) regression model is proposed and a survival data is used in an application of the proposed regression model. The log-GBXII(L) regression model is adequate and can be used in comparison to other models.