Journal of Statistical Modelling: Theory and Applications
Volume:3 Issue: 1, Winter and Spring 2022

Rayleigh distribution is one of the statistical distributions in real data modeling and is mostly used in reliability. In this paper, we derive Bayesian estimation and the reliability of Rayleigh distribution under the entropy loss function, and the risk of Bayesian estimator of its under the entropy loss function. Finally, we describe our results with a Monte Carlo numerical simulation.

In this paper‎, ‎a new bivariate family of distributions is proposed by mixing up the new family of heavy-tailed distributions approach with the Farlie-Gumble-Morgenstern copula‎. ‎The resultant family may be called the Farlie-Gumble-Morgenstern new family of heavy-tailed distributions‎. ‎For the proposed family‎, ‎some properties of the concomitants of generalized order statistics are obtained‎. ‎The joint distribution of concomitants is also derived‎. ‎Furthermore‎, ‎for this new family‎, ‎some properties of extropy for the concomitant of generalized order statistics are obtained‎. ‎The method of maximum likelihood estimation is implemented to obtain the estimators of the parameters‎. ‎Two sub-models are studied using the introduced approach.

In this paper, we provide the expectation of a function of the quadratic form of the multivariate skew Laplace distribution using the generalized Laguerre series that can be applied to compute the elements of the Fisher information matrix. Finally, we give a numerical example to obtain the expectation of this quadratic form.

This paper considers a parallel system that has a random number of units. The number of units follows a power series distribution which includes several distributions such as geometric, logarithmic and zero-truncated Poisson distributions. Pareto distribution is considered for the lifetime distribution of units. The optimal parameter is obtained for the distribution of sample size so that the expected cost is minimized and the whole reliability of the system is maximized. The weighted sum method has been utilized to convert this bi-objective model into a one-objective model. Numerical calculations have been performed to evaluate the obtained results.

In this paper‎, ‎we study a model of hypotheses testing consisting of two simple homogeneous stationary Markov chains with a finite number of states such that having different distributions from L≥ 2 possible transition probabilities‎. ‎The matrix of all possible pairs of asymptotical interdependence of the error probability exponents for logarithmically asymptotically optimal testing is determined‎. ‎For this aim‎, ‎we apply the method of type and large deviation techniques.

Evaluating the performance and ranking of the judiciary of the provinces periodically is always of interest‎. ‎This problem can be done with univariate approaches; But considering many variables involved in this matter‎, ‎the use of multivariate methods is more justified‎. ‎A new method for this is ranking based on the depth concept‎. ‎In this paper‎, ‎the performance of prosecutors' offices‎, ‎criminal courts and appeals courts of the provinces have been ranked over one year based on two indicators; case processing rate and the case congestion rate‎, ‎employing the depth multivariate method‎. ‎Evaluating the results of ranking intuitively confirms the appropriateness and rationality of this approach.

The functional linear regression model with points of impact is a recent augmentation of the classical functional linear model with many practically important applications‎. ‎It is assumed that there exists an unknown number of impact points‎, ‎that is discrete observation times where the corresponding functional values possess significant influences on the response variable‎. ‎In this paper‎, ‎we obtain some asymptotic properties of the model that can be used for further statistical inferences about the response variable‎. ‎Specifically‎, ‎rates of convergence for eigenfunctions estimates of the predictor covariance operator evaluated at the impact points estimates are derived‎. ‎These are important results‎, ‎because we do not have true eigenfunctions and impact points in applications and we have to use their estimates instead.

In this paper‎, ‎we introduce a novel family of statistical models called a new alpha power type-1 family of distributions‎. ‎Three sub-cases of the family are discussed‎. ‎Based on the novel family‎, ‎a special model‎, ‎explicitly‎, ‎a new alpha power type-1-Weibull distribution is studied in depth‎. ‎The new model has very interesting patterns of failure rates like increasing‎, ‎decreasing‎, ‎bathtub‎, ‎and parabola-down‎. ‎Hence‎, ‎it is so flexible‎. ‎Based on the comparison analysis‎, ‎among five well-known models‎, ‎it has an impact on health data analysis‎. ‎Furthermore‎, ‎the count data models capable of handling overdispersion and zero-inflation are discussed and applied the real health data‎. ‎The zero-inflated negative binomial model in the frequentist approach has shown its popularity in handling both overdispersion and zero-inflation simultaneously‎, ‎while the discrete Weibull model with the logit(q) link in the Bayesian approach outperformed its counterparts.

In this paper‎, ‎we consider the estimation of the stress-strength reliability of a coherent system‎. ‎The distributions of stress and strength random variables are the members of a general class of distributions‎. ‎For a series-parallel system‎, ‎the reliability of the stress-strength model is estimated using the maximum likelihood estimation‎, ‎asymptotic confidence interval‎, ‎uniformly minimum variance unbiased estimation‎, ‎and Bayes estimation‎. ‎Also‎, ‎simulation studies are performed‎, ‎and two real data sets are analyzed.

Statistical methods are practical and unavoidable in analysis of physical and engineering results‎. ‎Study of anufacturing errors and uncertainties in construction of radio frequency structures is one of cases which statistical quantities is used‎. ‎In this paper‎, ‎we quantify uncertainty in the cutoff frequency of a waveguide using the chaos polynomial expansion method‎. ‎Different distributions for uncertainty in the waveguide width are considered‎. ‎We then investigate the effect of the distributions on the waveguide cutoff frequency‎. ‎Using statistical quantities‎, ‎we determine the amount of acceptable error during the construction of the waveguide such that it does not affect the wavequide performance.

One of the most practical nonparametric methods in analysis of time series observations is the singular spectrum analysis method‎. ‎This method has been developed and applied to many practical problems across different fields and continuous efforts have been made to improve this method‎, ‎especially in forecasting‎. ‎In this paper‎, ‎the state space model and Kalman filter algorithms are used for noise elimination and time series smoothing‎. ‎Finally‎, ‎we compare these forecasting methods' abilities using the root mean squared error criteria for simulation studies and the real datasets.