Time series are essential for anticipating various claims payment applications. For insurance firms to prevent significant losses brought on by potential future claims, the future values of predicted claims are crucial. Additionally, the ideal parameter is chosen artificially. By using a genuine application, the proposed model’s utility is demonstrated. Additionally, the ideal parameter is chosen artificially. By using a genuine application, the proposed model's utility is demonstrated. Also, the single exponential smoothing model is used for prediction under the Holt-Winters’ additive algorithm.

Financial crisis prediction is a critical issue in the economic phenomenon. Correct predictions can provide the knowledge for stakeholders to make policies to preserve and increase economic stability. Several approaches for predicting the financial crisis have been developed. However, the classification model's performance and prediction accuracy, as well as legal data, are insufficient for usage in real applications. So that, an efficient prediction model is required for higher performance results. This paper adopts a novel two-hybrid intelligent prediction model using an Artificial Neural Network (ANN) for prediction and Particle Swarm Optimization (PSO) for optimization. At first, a PSO technique produces the hyperparameter value for ANN to fit the best architecture. They are weights and thresholds. Then, they are used to predict the performance of the given dataset.  In the end, ANN-PSO generates predictions value of crisis conditions. The proposed ANN-PSO model is implemented on time series data of economic conditions in Indonesia. Dataset was obtained from International Monetary Fund and the Indonesian Economic and Financial Statistics. Independent variable data using 13 potential indicators, namely imports, exports, trade exchange rates, foreign exchange reserves, the composite stock price index, real exchange rates, real deposit rates, bank deposits, loan and deposit interest rates, the difference between the real BI rate and the real FED rate, the M1, M2 multiplier, and the ratio of M2 to foreign exchange reserves. Meanwhile, the dependent variable uses the perfect signal value based on the Financial Pressure Index. A detailed statistical analysis of the dataset is also given by threshold value to convey crisis conditions. Experimental analysis shows that the proposed model is reliable based on the different evaluation criteria. The case studies show that the result for predictive data is basically consistent with the actual situation, which has greatly helped the prediction of a financial crisis.  

When a life test is terminated at a predetermined time to decide whether to accept or refuse the submitted batches, the types of group sampling inspection plans (single, two, and multiple-stages) are introduced. The tables in this study give the optimal number of groups for various confidence levels, examination limits, and values of the ratio of the determined experiment time to the fixed percentile life. At various quality levels, the operating characteristic functions and accompanying producer's risk are derived for various types of group sampling inspection plans. At the determined producer's risk, the optimal ratios of real percentile life to a fixed percentile life are obtained. Three case studies are provided to illustrate the processes described here. Comparisons of single-stage and iterative group sampling plans are introduced. The first, second, and third sample minimums must be used to guarantee that the product's stipulated mean and median lifetimes are reached at a certain degree of customer trust. The suggested sample plans' operational characteristic values and the producer's risk are given. In order to show how the suggested approaches based on the mean life span and median life span of the product may function in reality, certain real-world examples are examined.

After studying the mathematical properties of the Double Burr XII model, we present Bayesian and non-Bayesian estimation for its unknown parameters. Also, we constructed a new statistical test for goodness-of-fit in case of complete and censored samples. The modified test is developed based on the Nikulin-Rao-Robson statistic for validation. Simulations are performed for assessing the new test along with nine applications on real data.

In this paper we extend autoregressive models to fit time series that have three layers of seasonality, i.e. triple seasonal autoregressive (TSAR) models, and we introduce the Bayesian inference for these TSAR models. Assuming the TSAR model errors are normally distributed and employing three priors, i.e. Jeffreys', g, and normal-gamma priors, on the model parameters, we derive the marginal posterior distributions of the TSAR model parameters. In particular, we show that the marginal posterior distributions to be multivariate t and gamma distributions for the model coefficients and precision, respectively. We evaluate the efficiency of the proposed Bayesian inference using simulation study, and we then apply it to real-world hourly electricity load time series datasets in six European countries.

This paper proposes the 4-parameter odd Lomax generalized exponential distribution for the study of engineering and COVID-19 data. The statistical and mathematical properties of this distribution such as a linear representation of the probability density function, survival function, hazard rate function, moments, quantile function, order statistics, entropy, mean deviation, characteristic function, and average residual life function are established. The estimates of parameters of the proposed distribution are obtained using maximum likelihood estimation (MLE), Maximum product spacings (MPS), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. A Monte-Carlo simulation experiment is carried out to study the MLEs. The applicability of the proposed distribution is evaluated using two real datasets related to engineering and COVID-19. All the computational work was performed in R programming software.

In this paper, a new five-parameter model called alpha power exponentiated new Weibull-Pareto distribution is introduced based on a new developing technique. We derived some properties relating to the proposed distribution, including moments, moment generating function, quantile function, mean residual life and mean waiting time, and order statistics of the new model. The model parameters are estimated using the maximum likelihood method. Some simulation studies are performed to investigate the effectiveness of the estimates. Finally, we used three real-life data sets to show the flexibility of the introduced distribution.

Chen's model with bathtub shape provides an appropriate conceptual for the hazard rate of various industrial products and clinical cases. This article deals with the problem of estimating the model parameters, reliability and hazard functions of a three-parameter Chen distribution based on progressively Type-II censored sample have been obtained. Based on the s-normal approximation to the asymptotic distribution of the maximum likelihood estimates and log-transformed maximum likelihood estimates, the approximate confidence intervals for the unknown parameters, and any function of them, are constructed. Using independent gamma conjugate priors, the Bayes estimators of the unknown parameters and reliability characteristics are derived under different versions of a symmetric squared error loss functions. However, the Bayes estimators are obtained in a complex form, so we have been used Metropolis-Hastings sampler procedure to carry out the Bayes estimates and also to construct the corresponding credible intervals. To assess the performance of the proposed estimators, numerical results using Monte Carlo simulation study were reported. To determine the optimum censoring scheme among different competing censoring plans, some optimality criteria have been considered. A practical example using real-life data set, representing the survival times of head and neck cancer patients, is discussed to demonstrate how the applicability of the proposed methods in real phenomenon.

Analyzing the future values of anticipated claims is essential in order for insurance companies to avoid major losses caused by prospective future claims. This study proposes a novel three-parameter compound Lomax extension. The new density can be "monotonically declining", "symmetric", "bimodal-asymmetric", "asymmetric with right tail", "asymmetric with wide peak" or "asymmetric with left tail". The new hazard rate can take the following shapes: "J-shape", "bathtub (U-shape)", "upside down-increasing", "decreasing-constant", and "upside down-increasing". We use some common copulas, including the Farlie-Gumbel-Morgenstern copula, the Clayton copula, the modified Farlie-Gumbel-Morgenstern copula, Renyi's copula and Ali-Mikhail-Haq copula to present some new bivariate quasi-Poisson generalized Weibull Lomax distributions for the bivariate mathematical modelling. Relevant mathematical properties are determined, including mean waiting time, mean deviation, raw and incomplete moments, residual life moments, and moments of the reversed residual life. Two actual data sets are examined to demonstrate the unique Lomax extension's usefulness. The new model provides the lowest statistic testing based on two real data sets. The risk exposure under insurance claims data is characterized using five important risk indicators: value-at-risk, tail variance, tail-value-at-risk, tail mean-variance, and mean excess loss function. For the new model, these risk indicators are calculated. In accordance with five separate risk indicators, the insurance claims data are employed in risk analysis. We choose to focus on examining these data under five primary risk indicators since they have a straightforward tail to the left and only one peak. All risk indicators under the insurance claims data are addressed for numerical and graphical risk assessment and analysis.

A new three-parameter Nadarajah Haghighi model is introduced and studied. The new density has various shapes such as the right skewed, left skewed and symmetric and its corresponding hazard rate shapes can be increasing, decreasing, bathtub, upside down and constant. Characterization results are obtained based on two truncated moments and in terms of the hazard function. Validation via a modified chi-squared goodness-of-fit test is presented under the new model. A simple type Copula based construction is employed in deriving many bivariate and multivariate type distributions. The potentiality uncensored and censored real data sets. We constructed a modified Nikulin-Rao-Robson chi-square goodness-of-fit type test for the new model. This modi…ed chi-square test takes into account both unknown parameters and censorship. Validation in case of right censoring and all the elements constituting the test criteria. The censored aluminum reduction cells data is analyzed for validation.

The researchers in applied statistics are recently highly motivated to introduce new generalizations of distributions due to the limitations of the classical univariate distributions. In this study, we propose a new family called new generalized-X family of distributions. A special sub-model called new generalized-Weibull distribution is studied in detail. Some basic statistical properties are discussed in depth. The performance of the new proposed model is assessed graphically and numerically. It is compared with the five well-known competing models. The proposed model is the best in its performance based on the model adequacy and discrimination techniques. The analysis is done for the real data and the maximum likelihood estimation technique is used for the estimation of the model parameters. Furthermore, a simulation study is conducted to evaluate the performance of the maximum likelihood estimators. Additionally, we discuss a mixture of random effect models which are capable of dealing with the overdispersion and correlation in the data. The models are compared for their best fit of the data with these important features. The graphical and model comparison methods implied a good improvement in the combined model.

In this work, we introduced a new three-parameter Nadarajah-Haghighi model. We derived explicit expressions for some of it statistical properties. The Farlie Gumbel Morgenstern, modified Farlie Gumbel Morgenstern, Clayton, Renyi and Ali-Mikhail-Haq copulas are used for deriving some bivariate type extensions. We consider maximum likelihood, Cramér-von-Mises, ordinary least squares, whighted least squares, Anderson Darling, right tail Anderson Darling and left tail Anderson Darling estimation procedures to estimate the unknown model parameters. Simulation study for comparing estimation methods is performed. An application for comparing methods as also presented. The maximum likelihood estimation method is the best method. However, the other methods performed well. Another application for comparing the competitive models is investigated.

In this paper, we introduce the exponentiated generalized alpha power family of distributions to extend the several other distributions. We used the new family to discuss the exponentiated generalized alpha power exponential (EGAPEx) distribution. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by the maximum likelihood estimation (MLE), maximum product spacing (MPS) and Bayesian estimation methods. A Monte Carlo Simulation is performed to compare between different methods. We illustrate the performance of the proposed new family of distributions by means of two real data sets and the data sets show the new family of distributions is more appropriate as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions.

In this article, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index are performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "monotonically decreasing", " monotonically increasing", "increasing-constant”, “upside-down-constant", "decreasing-constant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The applicability of the new life distribution is illustrated by means of two real data sets.

The linear fractional transportation problem (LFTP) is widely encountered as a particular type of transportation problem (TP) in real-life. In this paper, a novel algorithm, based on the traditional definition of continuity, is presented to solve the LFTP. An iterative constraint is constructed by combining the objective function of the LFTP and the supply-demand condition since the fractional objective function is continuous at every point of the feasible region. By this constraint obtained, LFTP is converted into an iterative linear programming (LP) problem to reach the optimum solution. In this study, the case of asymptotic solution for LFTP is discussed for the first time in the literature. The numerical examples are performed for the linear and asymptotic cases to illustrate the method, and the approach proposed is compared with the other existing methods to demonstrate the efficiency of the algorithm. Also, an application had environmentalist objective is solved by proposed mathematical method using the software general algebraic modeling system (GAMS) with data set of the real case. Finally, some computational results from tests performed on randomly generated large-scale transportation problems are provided.

In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through the Kumaraswamy family. The proposed model is referred to as the Kumaraswamy extended exponential (KwEE). The significance of the suggested distribution from its flexibility in applications and data modeling. As specific sub-models, it includes the exponential, Kumaraswamy exponential, Kumaraswamy Lindley, Lindley, extended exponential, exponentiated Lindley, gamma and generalized exponential distributions. The representation of the density function, quantile function, ordinary and incomplete moments, generating function, and reliability of the KwEE distribution are all derived. The maximum likelihood approach is used to estimate model parameters. A simulation study for maximum likelihood estimates was used to investigate the behaviour of the model parameters. A numerical analysis is performed for various sample sizes and parameter values to analyze the behaviour of estimates using accuracy measures. According to a simulated investigation, the KwEE's maximum likelihood estimates perform well with increased sample size. We provide two real-world examples utilizing applied research to demonstrate that the new model is more effective.

A new class of distributions called Marshall-Olkin Zubair-G family is proposed in this study. Some statistical properties of the family are derived and two special distributions namely, Marshall-Olkin Zubair Nadarajah-Haghighi and Marshall-Olkin Zubair Weibull distributions are developed. The plots of the density and hazard rate functions of the special distributions exhibit different shapes for chosen parameter values, making them good candidates for modeling different types of datasets. A real life application using the Marshall-Olkin Zubair Nadarajah-Haghighi distribution revealed that it performs better than other existing extensions of the Nadarajah-Haghighi distribution for the given dataset.

In the present study, we propose a new family of distributions namely the Pareto-X family. A sub model of the proposed family called Pareto-Weibull (PW) distribution is discussed. The maximum likelihood estimators of the model parameters are obtained. Different distributional properties of the distribution are described. In order to assess the applicability of the model, two real-life applications from environmental and biological study are considered. The practical applications show that the proposed model provides better fitness than any other models used in this study.

In the past couple of years, statistical models have been extensively used in applied areas for analyzing real data sets. However, in numerous situations, the traditional distributions are not flexible enough to cater to different aspects of the real phenomena. For example, (i) in the practice of reliability engineering and biomedical analysis, some distributions provide the best fit to the data having monotonic failure rate function, but fails to provide the best fit to the data having non-monotonic failure rate function, (ii) some statistical distributions provide the best fit for small insurance losses, but fails to provide an adequate fit to large claim size data, and (iii) some distributions do not have closed forms causing difficulties in the estimation process. To address the above issues, therefore, several methods have been suggested to improve the flexibility of the classical distributions. In this article, we investigate some of the former methods of generalizing the existing distributions. Further, we propose nineteen new methods of extending the classical distributions to obtain flexible models suitable for modeling data in applied fields. We also provide certain characterizations of the newly proposed families. Finally, we provide a comparative study of the newly proposed and some other existing well-known models via analyzing three real data sets from three different disciplines such as reliability engineering, medical, and financial sciences.

The relationship between the reference-uncooperative linear bilevel two-follower decision making and the multi-objective decision making has been recently considered (Sadeghi and Moslemi, 2019). In this paper, we address the foregoing relation for the
 uncooperative linear bilevel multi-follower programming (ULBMFP) model with  followers. Furthermore, we consider some geometric properties of the feasible solutions set of the ULBMFP problem. Moreover an algorithm to find an optimal solution for the ULBMFP problem was proposed. Ultimately, some numerical examples to illustrate the proposed algorithm were provided.

In this paper, a modified Chi-square goodness-of-fit test called the modified Bagdonavičius-Nikulin goodness-of-fit test statistic is investigated and the applied for distributional validation under the right censored case. The new modified goodness-of-fit test is presented and applied for the right censored data sets. The algorithm of the censored Barzilai-Borwein is employed via a comprehensive simulation study for assessing validity of the new test. The modified Bagdonavičius-Nikulin test is applied to four real and right censored data sets. A new distribution is compared with many other competitive distributions under the new modified Bagdonavičius-Nikulin goodness-of-fit test statistic.

We propose the McDonald Lindley-Poisson distribution and derive some of its mathematical properties including explicit expressions for moments, generating and quantile functions, mean deviations, order statistics and their moments. Its model parameters are estimated by maximum likelihood. A simulation study investigates the performance of the estimates. The new distribution represents a more flexible model for lifetime data analysis than other existing models as proved empirically by means of two real data sets.

This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived.  Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.

In this article, we defined and studied a new distribution for modeling extreme value. Some of its mathematical properties are derived and analyzed. Simple types copula is employed for proposing many bivariate and multivariate type extensions. Method of the maximum likelihood estimation is employed to estimate the model parameters. Graphically, we perform the simulation experiments to assess of the finite sample behavior of the maximum likelihood estimations. Three applications are presented for measuring the flexibility of the new model is illustrated using three real data applications.