نشریه اندیشه آماری
سال بیست و هشتم شماره 1 (پیاپی 55، بهار و تابستان 1402)

This study aimed to apply the theory of planned behaviors on entrepreneurial tendencies and the effect of this tendency on the development of information technology among 18-30 years old Iranian youth in the winter of 1401. A part of the sample was based on the age group listed in the characteristics of mobile operators (18-30 years old) in Tehran province who received the questionnaire completely randomly using SMS system and sending the link address, and also another section was a of students aged 18-30 years old of The Islamic Azad University of South Tehran Branch, and the research questionnaire was provided to them. The validity of the questionnaire was confirmed by experts in ICT and its reliability was obtained based on Cronbach's alpha test with an alpha coefficient of at least 0.70 (criterion). The results showed that according to the theory of planned behaviors, entrepreneurial tendency has an effect on information technology development in Iranian youth aged 18-30 years.

Bootstrap is a computer-based resampling and statistical inference method that can provide an estimate for the uncertainty of distribution parameters and quantiles in a frequency analysis. In this article, in addition to calculating the bootstrap confidence interval for the quantiles with percentile bootstrap(BP), accelerated bias-corrected bootstrap(BCA) and t-bootstrap methods, calculating of the confidence interval is proposed using the bootstrap highest density method(HDI) for the probability distributions used in the hydrology data and we obtain the average length of the confidence interval as a criterion for evaluating the methods. To calculate the average length of the confidence interval with different methods, first, the best distribution among the widely used distributions is fitted to the original data, and the parameters of the fitted distribution are estimated by the maximum likelihood method, and from that we obtain the quantiles. Then we continue by repeating the simulated bootstrap samples until the probability of covering the real quantile reaches the nominal confidence level of 0.95. The simulation results show that the bootstrap highest density method gives the lowest average confidence interval length among all methods.In previous studies, the probability of coverage with the same number of samples as the original sample and the number of bootstrap repetitions (for example, 1000) have been obtained, and finally the coverage probability closest to the nominal value of 0.95 was chosen as the optimal state, while in this article, for Avoiding a large number of bootstrap iterations, considering the number of different samples n = 20, 40, 60, ..., 160 that are simulated from the mother distribution, we continue the number of iterations of the bootstrap samples only until reaching the coverage probability of 0.95. Usually, two-parameter distributions require fewer samples than three-parameter distributions. In terms of the number of necessary repetitions (B) to reach the 95% confidence level, the t-bootstrap method usually required fewer repetitions, although the implement time of this method was longer in R software. The best distribution for the data used in this research is the two-parameter distribution of Frechet, which was selected as the best distribution in 80% of the stations, which can be used for similar studies that deal with the maximum annual precipitation values. According to the fitted distributions for the data of different stations, the two-parameter distributions always fit the data better than the three-parameter distributions. In general, the widest confidence intervals were obtained with BCA and tbootstrap methods, and the shortest confidence intervals were obtained with HDI and BP methods. Also, in terms of the distribution used and the length of the confidence interval, the two-parameter Gamma distribution has provided shorter confidence intervals and the three-parameter GEV and LP3 distributions have provided wider confidence intervals.

‎The use of administrative resources in censuses provides the possibility of reducing costs‎, ‎improving data quality and producing information with a shorter time sequence‎. ‎The mentioned cases‎, ‎in addition to the annual monitoring of indicators of sustainable development goals‎, ‎can also play a significant role in meeting the growing needs of the country's planning and research system‎, ‎but there are many challenges in this regard‎, ‎one of the most important of which is the assessment of the quality of administrative data‎. ‎Quality assessment is the most important aspect of using registration and administrative data in the census‎, ‎and it is one of the necessities of the registers-based population and housing censuses‎, ‎where traditional quality assessment criteria cannot be used‎. ‎In other words‎, ‎despite the advantages of using register and administrative data in the census‎, ‎there are many key quality risks that need to be addressed and assessed before using them in the census‎. ‎In this paper‎, ‎the methods by which the national statistics offices can evaluate the quality of the data obtained from the registers with the aim of producing high-quality statistical outputs have been reviewed‎. ‎Therefore‎, ‎the tools and key indicators used to quantify the quality assessment in each of the four stages of quality assessment including source‎, ‎input data‎, ‎process and output in the census process are introduced‎.

Today, the diagnosis of diseases using artificial intelligence and machine learning algorithms are of great importance, because by using the data available in the study field of the desired disease, useful information and results can be obtained that reduce the occurrence of many deaths. Among these diseases, we can mention the diagnosis of diabetes, which has spread today due to the growth of urban life and the decrease in people's activity. So, it is very important to know whether a person is suffering from diabetes or not. In this article, the data set related to the information of people who have done the diabetes diagnosis test is used, this information is related to 520 people. People are classified into two groups based on whether their diabetes test result is positive or not, and Bayesian classification methods such as Bayesian Support Vector Machine, Naive Bayes, CNK and CatBoost ensemble classification method have been used to conclude which of these The methods can have a better ability to analyze the data and also to compare these methods use accuracy, precision, F1-score, recall, ROC diagram.

This paper explore some extropy properties of the lifetime of coherent systems with the assumption that the lifetime distribution of system components are independent and identically distributed. The presented results are obtained using the concept of system signature. To this aim, we first provide an expression for extropy of the lifetime of coherent systems. Then, stochastic extropy comparisons are discussed for coherent systems under the condition that both systems have the same characteristic structure. In cases where the number of system components is large or the system has a complex structure, it is difficult or time-consuming to obtain the exact extropy value of the system lifetime. Therefore, bounds are also obtained for extropy. In addition, a new criterion for selecting a preferred system based on relative extropy is proposed, which considers the lifetime of the desired system closest to the parallel system.

Variance and entropy are distinct metrics that are commonly used to measure the uncertainty of random variables. While the variance shows how a random variable spreads more than expected, the entropy measure measures the uncertainty of an information approach, in other words, it measures the average amount of information of a random variable.For both uniform and normal distributions, variance is a ratio of power entropy. Finding such a monotonic relationship between variance and entropy for a larger class of these two distributions is very important and useful in signal processing, machine learning, information theory, probability and statistics, for example, it is used to reduce the errors of estimators and choose a strategy. gives, on average, the greatest or nearly greatest reduction in the entropy of the distribution of the target location, and the effectiveness of this method is tested using simulations with mining assay models. In this article, the upper bound of the variance for single-mode distributions whose tails are heavier than the tails of exponential distributions is created with the help of power entropy

In ‎this ‎article, ‎queunig ‎model ‎‎$‎M/M/1‎$ ‎is ‎Considered, ‎in ‎which ‎the ‎innterarrival ‎of ‎customers ‎have ‎an ‎exponenial ‎disributon ‎with ‎the ‎parameter ‎‎$‎lambda‎$ ‎and ‎the ‎service ‎times‎ ‎have ‎an ‎exponenial ‎disributon with the ‎parameter ‎‎$‎mu‎$ ‎and ‎are ‎independent ‎of ‎the ‎interarrival ‎times.‎ ‎it ‎is ‎also ‎assumed ‎that ‎the ‎system ‎is ‎active ‎until ‎‎$‎T‎$‎. Then, under this stopping time Bayesian, ‎$‎E‎$‎-Bayesian and hierarchical Bayesian estima‎‏‎tion‎s of the traffic intensity parameter of this queuing model are obtained under the general entropy loss function and considering the gamma and erlang prior distributions for parameters ‎$‎lambda‎$ ‎and ‎‎$‎mu‎$‎, respicctively. Then, using numerical analysis and based on a new index, Bayesian, ‎$‎E‎$‎-Bayesian and hierarchical Bayesian estima‎‏‎tion‎s are compared.

The importance of statistics and its education in today’s world, which is full of information and data, is not hidden from anyone. Statistical thinking is the main core of correct understanding of statistical concepts, data analysis and interpretation of phenomena. With the aim of achieving a comprehensive definition of statistical thinking and determining its elements, the present research has studied the researches of the last thirty years. This descriptive research has been carried out in a qualitative metacomposite method to provide an insight into the totality of existing studies. Based on the entry criteria, 123 researches were identified between 1990 and 2022, and finally, after screening, 22 researches were selected for detailed review and analysis. According to the present metacomposite findings, the elements of statistical thinking are: 1) Being dataoriented:paying attention to data, identifying the need for data, collecting and considering data, different representations of data, and methods of converting them to each other. 2) Variability: Considering permanent changes in all phenomena. 3) Statistical inference: paying attention to the types of sampling, reasoning and inference using statistical models, including the use of statistical charts and generalizing the results from the sample to the population. [4) Analysis of the statistical context:combining the statistical problem with the context.

Given the limited energy resources globally, energy optimization is crucial. A significant portion of this energy is consumed by buildings. Therefore, the aim of this research is to explore the simultaneous factors affecting the heating and cooling of buildings. In the current research, 768 different residential buildings simulated with Ecotect software have been investigated. Joint regression model and exploratory data analysis methods were used to identify the influencing factors of the heating and cooling of buildings. Based on variables such as relative compactness, overall height, surface area, and roof of the buildings, a new variable called ”type” (building model) was introduced and shown to be one of the strongest factors affecting the heating and cooling of buildings. This variable is related to the shape of the building. In the joint regression model, it is assumed that the responses follow a multivariate normal distribution. Then this model is compared with separate regression models (without assuming responses correlation) and using Akaike’s information criterion and deviance information criterion, pointing to the superiority of the joint regression model. Additionally, the model parameters are estimated using the maximum likelihood estimation method and the amount of Akaike model compared to the separate model is a decrease of 0.0072%, which shows the superiority of the joint regression model. The deviance information criterion is equal to 0.001736%, and in comparison with the chi distribution, the null hypothesis is rejected to test the superiority of the models, which is regressed to the superiority of the joint model.

The statistical inference of the multi-component stress-strength parameter, $R_{s,k}$, is considered in the three-parameter Weibull distribution. The problem is studied in two cases. In the first case, assuming that the stress and strength variables have common shape and location parameters and non-common scale parameters and all these parameters are unknown, the maximum likelihood estimation and the Bayesian estimation of the parameter $‎R_{s,k}$ are investigated. In this case, as the Bayesian estimation does not have a closed form, it is approximated by two methods, Lindley and $mbox{MCMC}$. Also, asymptotic confidence intervals have been obtained. In the second case, assuming that the stress and strength variables have known common shape and location parameters and non-common and unknown scale parameters, the maximum likelihood estimation, the uniformly minimum variance unbiased estimators, the exact Bayesian estimation of the parameter $‎R_{s,k}$ and the asymptotic confidence interval is calculated. Finally, using Monte Carlo simulation, the performance of different estimators has been compared.

Actuarial studies treat insurance losses as random variables, and appropriate probabilistic models are sought to model them. Since losses are evaluated in terms of a unitary amount, distributions with positive support are typically used to model them. However, in practice, losses are often bounded due to policyholder conditions, which must be considered when modeling. While this is not a problem for univariate cases, it becomes complicated for multivariate cases. Copulas can be helpful in such situations, but studying the correlation is crucial in the first step. Therefore, this paper addresses the problem of investigating the effect of restricted losses on correlation in multivariate cases. The Pearson correlation coefficient is a widely used measure of linear correlation between variables. In this study, we examine the correlation between two random variables and investigate the estimator of the correlation coefficient. Furthermore, we analyze a real-world dataset from an Iranian insurance company, including losses due to physical damage and bodily injury as covered by third-party liability insurance. Upper and lower limits for both the Pearson correlation coefficient and its estimator were derived. The Copula method was employed to obtain the bounds for the correlation parameters, while order statistics were used to obtain the bounds for the sample correlation coefficient. Furthermore, two methods were used to determine the correlation between physical damage and bodily injury, and the results were compared. Our findings suggest that the commonly used upper and lower bounds of -1 and +1 for the Pearson correlation coefficient may not always apply to insurance losses. Instead, our analysis reveals that narrower bounds can be established for this measure in such cases. The results of this study provide important insights into modeling insurance losses in multivariate cases and have practical implications for risk management and pricing decisions in the insurance industry.

Risk means a situation in which there is a possibility of deviation from a predicted result. Insurance is one of the methods of risk exposure that leads to the transfer of all or part of the risk from the insured to the insurer. Insurance policies are usually classified into two types: personal and non-life (non-life) insurance. According to this classification, any insurance policy that deals with the health of the insured person or persons is a personal insurance policy, otherwise it will be a nonlife insurance policy. Many insurances in the insurance industry are classified as non-life insurances. Fire, automobile, engineering, shipping, oil and energy insurances are examples of these insurances. Explanation and calculation of three issues in risk models are very important: the ruin probability, the time of ruin and the amount of ruin. In this article, the main and well-known results that have been obtained so far in the field of non-life insurance; Emphasizing the possibility of ruin, it is given along with various examples.