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For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these processes. This generalization adds a parameter $alin (0, 1]$, and is called the fractional exponent of the process. In this thesis, we clearly derive the transition from standard Poisson process to its fractional generalization (fractional Poisson process (fPp)). The link fPp and $alpha$-stable density is established by solving an integral equation. The link then leads to an algorithm for generating fPp that discovering more interesting properties. Method-of-moments estimators for the intensity rate $mu$ and fractional order $alpha$ derived and showing asymptotic normality of the estimators and construction of the corresponding confidence interval. Then the properties of the estimators are then tested using simulated data.

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 ‎Censored samples are discussed in experiments of life-testing; i.e‎. ‎whenever the experimenter does not observe the failure times of all units placed on a life test‎. ‎In recent years‎, ‎inference based on censored sampling is considered‎, ‎so that about the parameters of various distributions such as ‎normal‎, ‎exponential‎, ‎gamma‎, ‎Rayleigh‎, ‎Weibull‎, ‎log normal‎, ‎inverse Gaussian‎, ‎logistic‎, ‎Laplace‎, ‎and Pareto‎, ‎has been inferred based on censored sampling‎.

‎In this paper‎, ‎a procedure for exact hypothesis testing and obtaining confidence interval for mean of the exponential distribution under Type-I progressive hybrid censoring is proposed‎. ‎Then‎, ‎performance of the proposed confidence interval is evaluated using simulation‎. ‎Finally‎, ‎the proposed procedures are performed on a data set‎.

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‎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.

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Over the last decades there have been, increasing challenges to the traditional census. Collecting information from every person in a country using traditional methods is a massive and costly exercise and thus a key concern. Further, reduced willingness amongst the population to respond to the census questionnaires and unexpected crises such as the Covid-19 pandemic have maked it increasingly difficult for NSOs to produce reliable figures with the necessary geographical and substantive detail.But developments of new technologies and approaches to data collection mean that there are also emerging opportunities. The increasing desire to use administrative resources in the implementation of censuses has made it possible to reduce costs, improve data quality, and produce frequent information on an annual basis. A study of the different approaches adopted by some countries in the Asia-Pacific region shows that administrative data are currently being used in different ways to support census operations. Examining these approaches will be very useful to help and guide for countries contemplating the use of or expansion of their use of administrative data for censuses. In this article, while reviewing the definition of register and the types of administrative registers used in register-based census, the proceedings taken in some countries in moving towards register-based census are presented.
 

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‎Small and medium enterprises play a significant role in creating job opportunities‎, ‎gross domestic product‎, ‎increasing the production of domestic products and exports‎, ‎and are considered one of the key pillars of achieving the economic growth and development of countries‎. ‎The purpose of this article is to explain the position of SMEs and their contribution in employment‎, ‎economy‎, ‎export and access to banking resources in some selected countries and compare them with the data available in Iran‎. ‎For this purpose‎, ‎the total number of micro and small establishment in the private sector of the country (less than 50 employees) and the number of their persons employed have been estimated using the data of the labour force survey during 10 years period‎, ‎and their values‎ ​‎​are predicted for 1404 using the double exponential smoothing method‎. ‎The results indicate that the number of establishments with less than 50 employees in private sector increased during the period under review‎, ‎and by 1404‎, ‎its ‏‎count‎ will reach 4,596,855‎, ‎so that the share of the number of persons employed in these establishments is predicted to be 82.6 ‎percent‎ in the 1404‎. ‎However‎, ‎the evidence shows that the share of these enterprises in bank facilities over the past years was only 4.5 percent‎, ‎which is very low compared to other countries‎. ‎The findings of this research are helpful for the support programs of the government for SMEs‎.