Journal of Statistical Modelling: Theory and Applications
Volume:3 Issue: 2, Summer and Autumn 2022

This paper considers the Type I hybrid censoring and investigates the optimal value for the sample size which is assumed as a truncated binomial random variable‎. ‎Rayleigh distribution is considered for the lifetime distribution‎. ‎Towards this end‎, ‎various factors can be considered and the most important is the sampling cost criterion‎. ‎Since the sample size is a random variable‎, ‎the optimal parameter of the random sample size is determined so that the total cost of the test does not exceed a pre-determined value‎. ‎Numerical calculations and a simulation study have been performed to evaluate the obtained results‎. ‎Finally‎, ‎the conclusion of the article is presented.

In order to investigate a series of data scenarios and determine the model governing the changes of a random variable over time‎, ‎according to the variables affecting it‎, ‎efficient methods have been developed in recent decades‎. ‎One of these methods is the generalized additive model‎. ‎By this modeling for data‎, ‎it is possible to check the behavior of the non-linear data and even predict the future‎. ‎In this article‎, ‎we intend to express this method non-parametrically‎, ‎in cases such as when the variable is independent‎, ‎time series‎, ‎or has a lag and implement the estimation of model parameters‎. ‎Moreover‎, ‎we will demonstrate the power and effectiveness of this method by presenting some examples.

In this paper‎, ‎we consider a diagonal form for the variances of errors in linear models‎. ‎This form contains the homogeneous and heterogeneous for the errors‎. ‎First‎, ‎an estimation for the variances is given‎, ‎and then a method is introduced for the hypothesis test of parameters in linear models‎. ‎Some applications of this method are presented.

The nonhomogeneous Poisson process is commonly utilized to model the occurrence of events over time‎. ‎The identification of nonhomogeneous Poisson process relies on the intensity function‎, ‎which can be difficult to determine‎. ‎A straightforward approach is to set the intensity function to a constant value‎, ‎resulting in a homogeneous Poisson process‎. ‎However‎, ‎it is crucial to assess the homogeneity of the intensity function through an appropriate test beforehand‎. ‎Failure to confirm homogeneity leads to an infinite-dimensional problem that cannot be comprehensively resolved‎. ‎In this study‎, ‎we analyzed data on the number of passengers using the Tehran metro‎. ‎Our homogeneity test showed a nonhomogeneous arrival rate of passengers‎, ‎prompting us to explore different functions to estimate the intensity function‎. ‎We considered four functions and used a piecewise function to determine the best intensity function‎. ‎Our findings showed significant differences between the two models‎, ‎highlighting the effectiveness of the piecewise function model in predicting the number of metro passengers.

The main focus of this paper is to extend the analysis of some ruin related problems to a class of state-space compound binomial risk models for a sequence of independent and identically distributed random variables of interclaim times when the claim occurrences are homogeneous‎. ‎First‎, ‎we obtain the mass function of a defective renewal sequence of random {Fn }n≥0 -stopping times‎, ‎using the compound binomial of aggregate claim amount together the net profit condition‎, ‎and compute the infinite time ruin probability with Markov property of risk process‎. ‎Moreover‎, ‎we derive the distribution of the time to ruin among many random variables associated with ruin using the convolution of claim amount and Lagrange’s implicit function theorem‎. ‎Lastly‎, ‎the theoretical results are illustrated with numerical computations‎.

In this paper‎, ‎the problem of inferencing the stress-strength reliability under the ranked set sampling and the simple random sampling from the levy distribution function is investigated‎. ‎The maximum likelihood estimators‎, ‎their asymptotic distributions‎, ‎and Bayes estimators are provided for the stress-strength reliability parameter‎. ‎Furthermore‎, ‎using a Monte Carlo simulation‎, ‎for both sampling methods‎, ‎namely‎, ‎simple random sampling and ranked set sampling‎, ‎the Bayes risk estimators and the efficiency of the obtained estimators are computed and compared.

The present paper considers a discrete-time risk model with a homogeneous‎, ‎irreducible‎, ‎and aperiodic Markov chain‎. ‎The general distribution of total claim amounts is influenced by the environmental Markov chain and in the i-th period the individual claim sizes are conditionally independent‎. ‎We obtain the recursive formulae for infinite time ruin probability using the technique of ordinary generating functions‎. ‎In addition‎, ‎we give some restrictions which under those the ruin will not happen‎. ‎In the last part‎, ‎we present some numerical illustrations for the results and give the practical problem through a fully developed case study in the domain of social insurance

The two-parameter discrete Weibull distribution is an important model especially in reliability studies when the data are reported on a discrete scale‎. ‎The hazard rate function of a discrete Weibull distribution is monotonically increasing and decreasing‎. ‎The present paper provides a family of parametric discrete distributions which is an infinite mixture of exponentiated discrete Weibull distributions‎, ‎and versatile in fitting increasing‎, ‎decreasing‎, ‎and bathtub-shaped failure rate models to different discrete life-test data‎. ‎Some important distributional properties of the model such as the moments‎, ‎order statistics‎, ‎and infinite divisibility are investigated and the parameters of the distribution are estimated by the maximum likelihood method‎. ‎In addition‎, ‎a real data set is analyzed to show the effectiveness of the model‎. ‎Finally we conclude the paper.

In this paper‎, ‎we consider a k-component coherent system while the system lifetimes are observed‎, ‎the system structure is known and the component lifetime follows the proportional hazard rate model‎. ‎We discuss the prediction problem based on Type-II censored coherent system lifetime data‎. ‎For predicting the future system failures‎, ‎we obtain the maximum likelihood predictor‎, ‎the best unbiased predictor‎, ‎the conditional median predictor and the Bayesian predictors‎. ‎As it seems that the integrals of the Bayes prediction do not possess closed forms‎, ‎the Metropolis-Hastings method is applied to approximating these integrals‎. ‎Different interval predictors based on classical and Bayesian approaches are derived‎. ‎A numerical example is presented to illustrate the prediction methods used in this paper‎. ‎A Monte Carlo simulation study is performed to evaluate and compare the performances of different prediction methods.

In Bayesian inference‎, ‎the acquisition of prior distributions plays a fundamental role‎. ‎While authorized priors need not conform to traditional probability densities and may be improper priors‎, ‎obtaining proper prior densities remains a challenge in the Bayesian literature‎. ‎This article explores a set of conditions that enable the establishment of specific assumptions‎, ‎ensuring that maximum entropy priors and restricted reference priors become proper and transform into probability density priors‎. ‎By examining these conditions‎, ‎this study contributes to the advancement of proper prior acquisition in Bayesian analysis.

In designing an optimal life-testing experiment under a censoring setup‎, ‎the removal vector scheme is usually chosen by optimizing a suitable criterion function‎. ‎The criterion functions are usually constructed based on cost or variance functions‎, ‎and sometimes a combination of both‎. ‎This paper considers a multiple optimization problem in the context of Type-II progressive censoring with random dependent removal lifetime experiment‎. ‎A simple simulation algorithm is presented for obtaining the optimal scheme in a multi-objective optimal problem under the Type-II progressive censoring with random dependent removal model‎. ‎Several simulation studies are conducted to evaluate and compare the performance of the proposed strategy‎. ‎Finally‎, ‎some concluding remarks and future works are provided.

The sinusoidal model has many applications in time series analysis‎, ‎signal processing‎, ‎regression‎, ‎and other phenomena that are repeated periodically‎. ‎On the other hand‎, ‎smoothing spline is a flexible and useful method in many fields‎. ‎In this article‎, ‎smoothing spline is applied to interpolate data generated from the sinusoidal model‎. ‎Therefore‎, ‎a sinusoidal model is considered in three general forms‎. ‎Then‎, ‎in a simulation study‎, ‎data sets are generated from each of the sinusoidal model forms‎, ‎and the effect of changing the model components is assessed‎. ‎Besides‎, ‎the smoothing spline method is applied to estimate the related sinusoidal model‎, ‎and the performance of the smoothing spline for fitting a proper model to the sinusoidal data is studied‎. Furthermore‎, ‎by fitting a proper sinusoidal model to each generated data set‎, ‎the performance of smoothing spline is compared with the sinusoidal model‎. The ‎sum of squares error criterion is applied to compare the performance of models‎. ‎The simulation results illustrate that smoothing spline has better performance for model fitting to sinusoidal data.