Journal of Statistical Modelling: Theory and Applications
https://jsm.yazd.ac.ir/
Journal of Statistical Modelling: Theory and Applicationsendaily1Fri, 01 Jul 2022 00:00:00 +0430Fri, 01 Jul 2022 00:00:00 +0430Optimality in Type I hybrid censoring with random sample size
https://jsm.yazd.ac.ir/article_3082.html
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&lrm;. &lrm;Rayleigh distribution is considered for the lifetime distribution&lrm;. &lrm;Towards this end&lrm;, &lrm;various factors can be considered and the most important is the sampling cost criterion&lrm;. &lrm;Since the sample size is a random variable&lrm;, &lrm;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&lrm;. &lrm;Numerical calculations and a simulation study have been performed to evaluate the obtained results&lrm;. &lrm;Finally&lrm;, &lrm;the conclusion of the article is presented.Introduction to non-parametric generalized additive models
https://jsm.yazd.ac.ir/article_3099.html
In order to investigate a series of data scenarios and determine the model governing the changes of a random variable over time&lrm;, &lrm;according to the variables affecting it&lrm;, &lrm;efficient methods have been developed in recent decades&lrm;. &lrm;One of these methods is the generalized additive model&lrm;. &lrm;By this modeling for data&lrm;, &lrm;it is possible to check the behavior of the non-linear data and even predict the future&lrm;. &lrm;In this article&lrm;, &lrm;we intend to express this method non-parametrically&lrm;, &lrm;in cases such as when the variable is independent&lrm;, &lrm;time series&lrm;, &lrm;or has a lag and implement the estimation of model parameters&lrm;. &lrm;Moreover&lrm;, &lrm;we will demonstrate the power and effectiveness of this method by presenting some examples.Inference on linear models with unequal variances
https://jsm.yazd.ac.ir/article_3100.html
In this paper&lrm;, &lrm;we consider a diagonal form for the variances of errors in linear models&lrm;. &lrm;This form contains the homogeneous and heterogeneous for the errors&lrm;. &lrm;First&lrm;, &lrm;an estimation for the variances is given&lrm;, &lrm;and then a method is introduced for the hypothesis test of parameters in linear models&lrm;. &lrm;Some applications of this method are presented.Predicting intensity function of nonhomogeneous Poisson process
https://jsm.yazd.ac.ir/article_3124.html
The nonhomogeneous Poisson process is commonly utilized to model the occurrence of events over time&lrm;. &lrm;The identification of nonhomogeneous Poisson process relies on the intensity function&lrm;, &lrm;which can be difficult to determine&lrm;. &lrm;A straightforward approach is to set the intensity function to a constant value&lrm;, &lrm;resulting in a homogeneous Poisson process&lrm;. &lrm;However&lrm;, &lrm;it is crucial to assess the homogeneity of the intensity function through an appropriate test beforehand&lrm;. &lrm;Failure to confirm homogeneity leads to an infinite-dimensional problem that cannot be comprehensively resolved&lrm;. &lrm;In this study&lrm;, &lrm;we analyzed data on the number of passengers using the Tehran metro&lrm;. &lrm;Our homogeneity test showed a nonhomogeneous arrival rate of passengers&lrm;, &lrm;prompting us to explore different functions to estimate the intensity function&lrm;. &lrm;We considered four functions and used a piecewise function to determine the best intensity function&lrm;. &lrm;Our findings showed significant differences between the two models&lrm;, &lrm;highlighting the effectiveness of the piecewise function model in predicting the number of metro passengers.Ruin related quantities in a class of state-space compound binomial models
https://jsm.yazd.ac.ir/article_3128.html
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&lrm;. &lrm;First&lrm;, &lrm;we obtain the mass function of a defective renewal sequence of random {Fn }n&ge;0 -stopping times&lrm;, &lrm;using the compound binomial of aggregate claim amount together the net profit condition&lrm;, &lrm;and compute the infinite time ruin probability with Markov property of risk process&lrm;. &lrm;Moreover&lrm;, &lrm;we derive the distribution of the time to ruin among many random variables associated with ruin using the convolution of claim amount and Lagrange&rsquo;s implicit function theorem&lrm;. &lrm;Lastly&lrm;, &lrm;the theoretical results are illustrated with numerical computations&lrm;.Estimation of the stress-strength reliability for the Levy distribution based on the ranked set sampling
https://jsm.yazd.ac.ir/article_3153.html
In this paper&lrm;, &lrm;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&lrm;. &lrm;The maximum likelihood estimators&lrm;, &lrm;their asymptotic distributions&lrm;, &lrm;and Bayes estimators are provided for the stress-strength reliability parameter&lrm;. &lrm;Furthermore&lrm;, &lrm;using a Monte Carlo simulation&lrm;, &lrm;for both sampling methods&lrm;, &lrm;namely&lrm;, &lrm;simple random sampling and ranked set sampling&lrm;, &lrm;the Bayes risk estimators and the efficiency of the obtained estimators are computed and compared.Ruin probabilities in a discrete-time risk process with homogeneous markov chain
https://jsm.yazd.ac.ir/article_3162.html
The present paper considers a discrete-time risk model with a homogeneous&lrm;, &lrm;irreducible&lrm;, &lrm;and aperiodic Markov chain&lrm;. &lrm;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&lrm;. &lrm;We obtain the recursive formulae for infinite time ruin probability using the technique of ordinary generating functions&lrm;. &lrm;In addition&lrm;, &lrm;we give some restrictions which under those the ruin will not happen&lrm;. &lrm;In the last part&lrm;, &lrm;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