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03- Journal of Statistics Applications & Probability



Interval Estimation for Burr Type-X distribution under Type-I hybrid progressive censoring scheme

M. M. Amein, Neveen Sayed-Ahmed, Ohoud Sami Bakri,
Abstract :
In this research, point and interval estimation for unknown parameters of Burr Type-X (Burr-X) distribution based on the Type-I hybrid progressive censoring are obtained . For the estimation process, the maximum likelihood estimations (MLEs) and Bayesian methods (BM) with Markov Chain Monte Carlo (MCMC) are used. Finally, some computations and comparisons between the different methods based on simulation data are obtained.


Churn Prediction for Savings Bank Customers: A Machine Learning Approach

Prashant Verma,
Abstract :
Commercial banks are facing immense pressure, including financial disintermediation, interest rate volatility and digital ways of finance. Acquiring a new customer is anywhere from 5 to 25 times more expensive than retaining an existing one. Commercial banks must avoid customer churn while acquiring new customers, to expand their business and enhance their core competitiveness. This paper explores savings account customer churn prediction, based on various statistical & machine learning models and uses under-sampling, to improve the predictive power of these models, considering the imbalance characteristics of customer churn rate in the data. Model Accuracy, Area under the curve (AUC), Gini coefficient, and Receiver Operating Characteristics (ROC) curve have been utilized for model comparison. The results show that out of the various machine learning models, Random Forest which predicts the churn with 78% accuracy, has been found to be the most powerful model for the scenario. Customer vintage, customer’s age, average balance, occupation code, population code, average debit amount, and an average number of transactions are found to be the variables with high predictive power for the churn prediction model. The model can be deployed by the commercial banks in order to avoid the customer churn so that they may retain the funds, which are kept by savings bank (SB) customers. The article suggests a customized campaign to be initiated by commercial banks to avoid SB customer churn. Hence, by giving better customer satisfaction and experience, the commercial banks can limit the customer churn and maintain their deposits.


Certain Results of (p,q)-analogue of Aleph-function with (p,q)-Derivative

Altaf Ahmad Bhat,
Abstract :
In this paper, the authors have derived the (p,q)-analogue of Aleph-Function with (p,q)-derivative by using the generalization of the Gamma and Beta functions. Some particular cases of these results in terms of (p,q)- analogue of G-Function, established earlier by Swati et. al. and I, Hfunctions, derived earlier by Altaf et. al. have also been obtained.


Inferences for Weibull-Gamma Distribution in Presence of Partially Accelerated Life Test

Rashad M. EL-Sagheer, Mohamed A. W. Mahmoud, Mahmoud M. M. Mansour,
Abstract :
In this paper, the point at issue of this paper is to deliberate point and interval estimations for the parameters of Weibull- Gamma distribution (WGD) using progressively Type-II censored (PROG-II-C) sample under step stress partially accelerated life test (SSPALT) model. The maximum likelihood (ML), Bayes, and four parametric bootstrap methods are used to obtain the point estimations for the distribution parameters and the acceleration factor. Furthermore, the approximate confidence intervals (ACIs), four bootstrap confidence intervals and credible intervals of the estimators have been got. The results of Bayes estimators are computed under the squared error loss (SEL) function using Markov Chain Monte Carlo (MCMC) method. Gibbs within the Metropolis–Hasting algorithm is applied to generate MCMC samples from the posterior density functions. Simulation results are carried out to explicate the precision of the estimators for the aforementioned parameters.


Implementing Logarithmic Type Estimation Procedure For Population Mean in Successive Sampling

Partha Mukhopadhyay,
Abstract :
Bahl, S. and Tuteja R.K. (1991) introduced exponential structure which earned considerable success among the survey statisticians. The present paper, getting inspiration from that, attempts to introduce a new chain type ratio estimator using logarithmic function structure. The estimator has been applied in successive sampling situation where complete response is presumed at both occasions. We have studied the properties of the suggested estimator and also derived its optimum condition. The strength of the proposed estimator over the conventional ones has been discussed through numerical illustrations pondering four standard data sets from various situations. Encouraged with the outcomes of the proposed estimator and strategy, it has been suggested to the survey statisticians for future use.


Analysis of Progressively Type-I Censored Data in Competing Risks Models with Generalized Inverted Exponential Distribution

Ahmed El-Saeed,
Abstract :
This paper presents estimates of the parameters included in a competing risks model in the presence of progressive type-I censored data. We consider the case when the competing risks have generalized inverted exponential distributions. The maximum likelihood method is used to derive point and asymptotic confidence intervals for the unknown parameters. The relative risks due to each cause of failure are investigated. A real data set is used to illustrate the theoretical results and to assess the performance of relative risk and MLE estimates at different schemes of progressively type-I censored samples under causes of failure follow the generalized inverted exponential distributions.


Accelerated Life Test Plans and Age-Replacement Policy under Warranty on Burr Type-X distribution with Type-II Censoring

Intekhab Alam,
Abstract :
In this paper, we describe how to design and analyze the accelerated life testing (ALTg) plans for the improvement of the quality and the reliability of the product. We also focus on finding the expected cost rate and the expected total cost for age-replacement under warranty policy. The problem is studied using constant stress, under the assumption that the lifetimes of the units follow Burr type-X distribution for predicting the cost of age replacement under warranty policy. Asymptotic variance and covariance matrix of the estimators are obtained by using the Fisher Information Matrix. Confidence intervals for parameters and respective errors are also obtained. A simulation study is performed to illustrate the statistical properties of the parameters and confidence bound. In the last, numerical examples are also carried out to illustrate the theoretical results.


Step Stress Partially Accelerated Life Tests and Estimating Costs of Maintenance Service Policy for the Power Function Distribution under Progressive Type-II Censoring

Intekhab Alam,
Abstract :
In this paper, we describe how to analyze and design the accelerated life testing (ALTg) plans for the improvement of the quality and the reliability of the product. We focus on estimating the costs of maintenance service policy because this policy plays a very important role to assist any manufacturing organization for sale and available its equipment’s and maintenance cost effective. When the lifetime of units follows the Power function distribution, then the partially step-stress stress accelerated life test is assumed. The maximum likelihood estimates (MLEs) are obtained under the progressive type-II censoring. By the use of the Fisher Information matrix, the asymptotic variance and covariance matrix is obtained. The confidence intervals (CIs) of the estimators are also constructed. At last, a simulation study is carried out to check the accuracy of the results.


Attribute Control Charts for the New Weibull Pareto Distribution Under Truncated Life Tests

Enayat M. Abd Elrazik,
Abstract :
An attribute control chart is developed in this paper for the new Weibull pareto distribution under truncated life tests. the performance of the new Weibull pareto distribution control chart constructed on truncated life test is evaluated by average run length (ARL), which compares the performance of the new Weibull pareto distribution with inverse gaussian.


Likelihood of Surviving Children using a Probability Model

Shubhagata Roy,
Abstract :
The decisions regarding future fertility preferences of couples are governed by the number of surviving children rather than the number of total children ever born. Hence, it is important to have the distribution of number of surviving children with the help of a concrete probability model. Although, a number of probability models are available to study the variation in the number of births to a female under varying sets of assumptions, but a very little work has been done to find out the distribution of number of surviving children out of the births in a given period of time. It is thus, desirable to develop a probability model which could explain the distribution of number of surviving children apart from deriving the distribution of number of births.


Statistical Analysis of Fertility Control Measures in Diverse Group of Females

Brijesh P. Singh, Sonam Maheshwari, Puneet Kumar Gupta,
Abstract :
Fertility in India will continue to decline steadily to below-replacement levels towards the end of the century, and then recover early next century. Averages aggregated at the national level however, mask the considerable economic, cultural and spatial heterogeneity at the regional level, which in turn, have a profound influence on the level and pace of fertility decline. Conventional fertility theories highlight the influence of modernization, social and economic development and diffusion of changing ideas and individualistic values on the desired number of children. In this study estimation of fertility pattern is analyzed by two fertility control measure. First measure is based on the birth interval treated as non–homogenous Poisson Process and second measure is based on ASFR. The results indicate fertility after age 35 is decreasing; it may be due to use of contraception or curtailing fertility after age 35 years.


A New Transmuted Lifetime Distribution: Statistical Properties and Application to Survival Data

Pawan Kumar,
Abstract :
In statistical literature, several methods are available to generate a new probability distribution by introducing new parameter to any existing standard distribution. The quadratic rank transmutation map method is one of these and received considerable attention in the literature. Here, we also proposed a new probability distribution using this method when DUSE(θ)-distribution is chosen as baseline distribution. The proposed distribution is called transmuted DUSE(θ)-distribution, which is seems to be more flexible as compared to the baseline distribution. Different statistical properties such as moments, quantile function, survival function, hazard function and order statistics have been derived. Also, the method of maximum likelihood and method of maximum product spacing are used to estimate the unknown parameters of the introduced probability distribution. Simulation study is being carried out to know the long-run behavior of the distribution. Finally, a real data set has been utilized to show the applicability of the proposed distribution.


MG Exponentiated Pareto Distribution

Hussein Eledum, S. I. Ansari,
Abstract :
In this paper, we have introduced a new generalization of the Exponentiated Pareto distribution named as the MG Exponentiated Pareto (MGEP) distribution based on MG transmutation map introduced by Kumar et al. (2017). Furthermore, we have derived some statistical properties of the MGEP distribution. The estimation of distribution parameters has been done by using maximum likelihood method and the performance of estimators is studies by using simulation. A real data have been studied for the importance of the new distribution.


A Generalization of Transmuted Laplace Distribution

Salwa Radwan,
Abstract :
Two new parameters are added to the Transmuted Laplace distribution, the proposed model is named the Generalized Transmuted Laplace distribution. The statistical properties are studied; providing the moments, moment generating function and differential entropy. Estimation of parameters using the maximum likelihood method are discussed. A real data set is used to show that the new distribution is a better model.


Piecewise Baseline Hazard Model with Gamma Frailty: Analysing the Transitions into The Labour Force Entry by The Youths in India

Jayanta Deb,
Abstract :
The present paper demonstrates piecewise constant baseline hazard model with shared frailty for analysing the timing of entry into workforce after schooling that are clustered into geographical domain. Observations from the same cluster are usually correlated because unknowingly they share certain unobserved characteristics. Including these within cluster correlations in the model allows correctly measuring the covariate effects and avoiding underestimation or overestimation of the parameters of interest. Besides analysing the effect of substantial demographic and socio-economic circumstances on the time to entry into the workforce for geographically clustered event history data, comparison of estimates obtained from the Cox regression model, the Cox regression model with shared frailty, and the piecewise constant baseline hazard with shared frailty are also outlined here.


A Probability Model for the Number of Female Child Births among Females

Anup Kumar,
Abstract :
We analysed the phenomenon of `son preference that is prevalent in the Indian society, through a probability model for the number of female child births among females of Indian society. In Rai et al. (2014) a probability model for the number of female childbirths was applied to an observed set of data taken from NFHS-III (2005-06) for the seven North-East states of India. Some problem regarding the application of the model to the data set is found and the proper solution is suggested. The modified approach is illustrated to observed data set taken from NFHS- III(2005-06) for few states of India of different regions.


Estimation of Generalized Inverted Exponential Distribution based on Adaptive Type-II Progressive Censoring Data

Al-Wageh A. Farghal,
Abstract :
In this paper, we consider generalized inverted exponential (GIE) model. Three issues represent the purpose of this paper. First, based on adaptive progressively Type-II censored data, we derive the maximum likelihood estimators (MLE) of the model parameters as well as the reliability and hzarard rat functions. Next, the Bayes estimates are evaluated by applying Markov Chain Monte Carlo method under the balanced squared error loss (BSEL) function and balanced linear exponential loss (BLINEX) function. Based on the asymptotic distributions of the MLEs and MCMC samples, we compute asymptotic confidence interval and symmetric credible interval along with the coverage probability. We analyse a real data set to illustrate the results derived. Simulation studies are conducted to compare the performances of the Bayes estimators with the maximum likelihood estimators. Finally, a numerical example is presented to illustrate the methods developed here.


On Characterization of Modified Weibull Distribution

Nagwa Mohamed,
Abstract :
This paper is devoted to derive some recurrence relations for single and product moments of generalized order statistics (Gos) for modified Weibull distribution (MWD). Based on these recurrence relations some characterizations for this distribution are discussed


Upgraded Family of Estimators of Population Mean under Simple Random Sampling Scheme using Known Parameters of Auxiliary and Study Variable

S.K. Yadav, Shanya Baghel,
Abstract :
The present paper consists of an improved class of estimators for population mean of study variable using the information related to an auxiliary variable, combined with the median of the study variable under the Simple Random Sampling Scheme. We have shown that many of the existing estimators of population mean are the members of the proposed class. The Bias and Mean Squared Error (MSE) of the suggested class are derived up to the first order of approximation. The Bias and the Minimum value of the MSE are obtained by optimizing the characterizing scalar. Bias and MSE has also been compared with the existing estimators. Finally we suggest some new members of the proposed class of estimators which are more efficient than the existing competing estimators numerically.



Mritunjay Pal Singh,
Abstract :
Migration is the least explored area of study of population change. The concept of migration includes a series of factors regarding place of origin and destination, intervening obstacles and personal characteristics. This paper is an attempt to study the migration at household level with the help of some statistical models. The models used in the study has been tested with the help of primary data collected by the authors in North-Eastern Bihar during 2009-10.


Parameter Estimation for a Mixture of Inverse Chen and Inverse Compound Rayleigh Distributions Based on Type-II Hybrid Censoring Scheme

Mohamed Mahmoud Mohamed Mahmoud,
Abstract :
The Bayesian estimation procedure for two-component mixture of the inverse Chen and inverse compound Rayleigh distributions(ICICRD), based on Type II hybrid censoring scheme is discussed. We derive maximum likelihood estimators and the approximate confidence intervals using asymptotic variance and covariance matrix. The Bayesian point estimation relative to symmetric squared error(SE) loss function and asymmetric linear exponential (LINEX) and general entropy (GE) loss functions, and highest posterior density credible interval of the parameters are obtained. We perform Monte Carlo simulation to compare the performances of the different estimates. Further, we consider the problem of predicting the future order statistics. Numerical results using generated data sets are presented.


A New Generalization of the Moyal Distribution

Mohamed Ibrahem,
Abstract :
In this article, a three parameter generalization of Moyal distribution is obtained, with the purpose of obtaining a more flexible model relative to the behaviour of hazard rate functions. Various statistical properties such as density, hazard rate functions, quantile function, mode, moments, incomplete moments, moment generating functions, mean deviation, Lorenz, Bonferroni and Zenga curves, Renyi and continuous entropies and distribution of rth order statistics have been derived. The method of maximum likelihood estimation has been used to estimate the parameters of the generalized Moyal distribution. Further confidence intervals are also obtained. Finally applicability of the proposed model to the real data is analyzed. A comparison has also been made with some existing distributions.


Temporal Variation of Temperature in Guwahati, Assam: An Application of Seasonal ARIMA Model

Utpal Dhar Das,
Abstract :
Analysis of time series has become major tool in various applications in environmental areas to understand phenomena, like rainfall, temperature, humidity, draught etc. Here SARIMA model has been used to carry out short-term predictions of monthly maximum and minimum temperature in Guwahati city of Assam. The present study aimed at analysing the temporal variation in temperature in Guwahati during the period 1981–2010. The study of linear trend indicated increasing trends in mean and maximum temperatures and decreasing trends in minimum temperatures, Mann-Kendall test has been used to know the variability in trends in annual and seasonal temperature. The analysis reveals that both seasonal and annual pattern, increasing tendency in temperature during the period 1981-2010. The analysis of moving average indicated two periods when annual mean temperature increased significantly. These periods are closely associated with the post-independence period of industrialization (1955-1965) and recent phase of urbanization (after 2000). The analysis also indicates that the rate of change in temperatures brought by post-independence period of industrial activities is higher than that of recent year’s urbanization. Again, the monthly and seasonal analysis of temperature revealed a sharp decline in minimum temperature during winter season and especially in the coldest month (January) than any other seasons.


Control Charts Based on Exponentiated Mukherjee-Islam Distribution

Amin Shaka Aunali, Venkatesan D.,
Abstract :
In Manufacturing, usually has three stages: production, inspection and packaging. The production may be performed by a series of components. The products of each component may be inspected by sub-components working in parallel. The products inspected by each sub-component may be packaged by a series of sub-sub-components. Control charts are useful for monitoring process statistics over time and detecting presence of special causes. A special cause causes variations that can be detected and verified. However, if the control chart indicates that the process has shifted, appropriate actions must be taken to regain control. Therefore, a control chart indicates the right time or to which observation corrective action should be taken. The use of control charts designed for a normal distribution may not be workable in this situation and may result in an increasing of the number of non-conforming products. In this paper, the concept of two parameters to generate new distributions which is the exponentiated Mukherjee-Islam distribution, have been used to the applications of statistical process control to check the performances of the process control when the process is not normal.


Statistical Analysis of Political and Economic Dimension of the Suez Canal Axis Development Project

Mahmoud Khalifa, Nasr Salem,
Abstract :
In this paper, we introduce a descriptive analytical method to identify the importance of foreign direct investment (FDI) and its political and economic determinants and the use of quantitative analysis to determine the expected impact of foreign direct investment in Suez Canal Development Project on the overall development in Egypt. It is shown that development of human resources to provide skilled and trained workers, skills and experience, develop a strategy to maximize value added activities and achieve maximum productivity to increase competitiveness. Also, providing an attractive investment environment, develop an integrated strategy to deal with economies of scale in all areas of activity and work on the stability of financial transactions and political and social stability will allow goods to pass directly from the port to the logistics center.


Bound Lengths on Type-I Progressive Hybrid Rayleigh Data under SS-PALT

Dr Gyan Prakash,
Abstract :
Present article discussed about some Bayes prediction bound lengths in one-parameter Rayleigh distribution. For this, Type-I Progressive Hybrid censoring criterion (T-IPH Censoring) have combined with Step-Stress Partially Accelerated Life Test (SS-PALT). Any literature has not found, for observing the Bayes prediction bound lengths under T-IPH Censoring with SS-PALT. One-Sample & Two-Sample Bayes prediction bound lengths have obtained in the above scenario. The analysis under simulated and real data set, by using Metropolis–Hastings (M-H) algorithm has discussed. The optimal stress change time also have measured by the method of minimization of the asymptotic variance of ML Estimation. Approximate confidence lengths (ACL) also have been discussed along with Bayes prediction bound lengths.


On a Bivariate Fréchet Distribution

Ehab M. Almetwally,
Abstract :
The bivariate Fréchet distribution is an important lifetime distribution in survival analysis. In this paper, Farlie–Gumbel–Morgenstern (FGM), Ali–Mikhail–Haq (AMH) copulas and Fréchet marginal distribution are used for creating bivariate distributions which are called FGM Bivariate Fréchet (FGMBF) and AMH Bivariate Fréchet (AMHBF) distributions. The reliability function and hazard function will be obtained for Bivariate Fréchet distributions. They are a good alternative to bivariate several lifetime distributions for modeling real-valued data in application. Some properties of the FGMBF distribution are obtained such as product moment and moment generation function. Two different estimation methods for the unknown parameters of the two Bivariate Fréchet models will be discussed. Asymptotic and bootstrap confidence intervals for the models parameter are also considered. To evaluate the performance of the estimators, a Monte Carlo simulations study is conducted to compare the efficiency between the two models and the preferences between estimation methods. Also, a two real data set are analyzed to investigate the models and useful results are obtained for illustrative purposes.


Sequential Testing Procedure for the Rate Parameter of Left Truncated Exponential Distribution

Mukesh Kumar,
Abstract :
Sequential testing procedure is used for rate parameter of left truncated exponential distribution (LTED). Sequential Probability Ratio Test (SPRT) is used for testing the hypothesis regarding the parameter of LTED. The expressions for the operating characteristic (OC) and average sample number (ASN) functions are derived and results are presented through tables and graphs.


Model suitability analysis of survival time to ovarian cancer patients data

Manoj Kumar,
Abstract :
In this paper, we propose a suitable statistical model for survival time of the ovarian cancer patients. The proposition follows by checking the suitability of the model through different statistical tools like the value of logarithmic of likelihood, Akaike Information Criterion, Kolmogorov-Smirnov distance, Bayesian Information Criterion. The maximum likelihood estimate of the parameters of the compared models has been obtained for the considered real data set. The non-parametric procedure has been used to show its applicability.


Estimation of Finite Population Mean Through A Two-Parameter Ratio- Product-Ratio-Type Exponential Estimator in Systematic Sampling

Housila, P. Singh, Anita Yadav,
Abstract :
In this paper, we suggest a two parameter ratio-product-ratio-type exponential estimator for estimating the finite population mean in systematic sampling. The bias and mean squared error of the suggested estimator are obtained to the first degree of approximation. It has been shown that the proposed estimator is better than the usual unbiased estimator, Swain’s (1964) ratio estimator, Shukla’s (1971) product estimator and Singh et al’s (2011) estimators under some realistic conditions. An empirical study has been under taken to evaluate the performance of the suggested estimator over other existing estimators.


Some Median Type Estimators to Estimate the Finite Population Mean

Javid Shabbir,
Abstract :
On the lines of Bahl and Tuteja (1991) and Grover and Kaur (2011) we propose new median based estimator to estimate f nite population mean in absence of the auxiliary variable. By using median approach the expressions for bias and mean squared error (MSE) are derived up to rst order approximation. In empirical and simulation study the comparison of median based proposed class of estimators with sample mean, ratio and linear regression estimators are discussed.

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