Determining the Pension Benefit Obligation of a Defined Benefit Plan: Applying a Multivariate ARIMA Stochastic Model

<p>In this study we examine the robustness of fit for a multivariate and an autoregressive integrated moving average model to a data sample time series type. The sample is a recurrent actuarial data set for a 10-year horizon. We utilize this methodology to contrast with stochastic models to make projections beyond the data horizon. Our key results suggest that both types of models are useful for making predictions of actuarial liability levels given by PBO Projected Benefit Obligations on and off the horizon of the sample time series. As we have seen in prior research, the use of multivariate models for control and auditing purposes is widely recommended. Fast and reliable statistical estimates are desirable in all cases, whether for audit purposes or to verify and validate miscellaneous actuarial results.</p>

Using Fishburne’s sequences in suitable modeling used for sample data

This article deals with probabilistic and statistical modeling of managerial decision-making in the economy based on sample data for the previous periods of time. For better definition, the study is limited to Markowitz’s models in the problem of finding an effective portfolio of the field in the third information situation. The third information situation is a widespread decision-making situation and is characterized by the fact that the decision-maker sets, according to his opinion, are a linear order relation on the components of an unknown probabilistic distribution of the states of the economic environment. Often, from the point of view of the decision-maker, the components of an unknown probability distribution of the states of the economic environment must satisfy a partially reinforced linear order relation. As a result, the use of traditional statistical estimates turns out to be impossible, while the following question arises, which is practically not studied in the scientific literature. In this case, what formulas should be used to find statistical estimates and, above all, estimates of unknown probabilities of the state of the economic environment? As an estimate of an unknown probability distribution, we proposed to use the Fishburne sequence that satisfies all available constraints, while corresponding to the opinion of the decision maker and the linear order relation given by him. Fishburne sequences are a generalization of the well-known Fishburne formulas. It is fundamentally important that any Fishburne sequence satisfies a simple linear order relation, and under certain conditions, a partially strengthened linear order relation. Particular attention is paid to the entropic properties of generalized Fishburne progressions, which represent the most important class of Fishburne sequences, as well as the use of generalized Fishburne progressions to take into account the opinion of the decision maker. Such a scheme for estimating an unknown probability distribution has been developed, which makes it possible to achieve the correctness of probabilistic and statistical modeling, as well as appropriate consideration of the opinion of the decision-maker, uncertainty and risk.

Statistical estimates bias for data with missing values: Nonresponse study: انحياز التقديرات الإحصائية للبيانات التي تحوي قيماً مفقودة: دراسة حالة عدم الاستجابة

Statistical surveys are usually conducted to obtain data describing a problem in a studied society, and many surveys experience a rise in nonresponse rates, as the rate of nonresponse may affect the bias of the nonresponse in survey estimates. Recent empirical results show instances of nonresponse rate correlation with nonresponse bias, we attempt to translate statistical experiences of nonresponse bias in newly published studies and research into causal models that lead to assumptions about when a lack of response causes bias in estimates. Research studies of the estimates of nonresponse bias show that this bias often exists. The logical question is: what is the advantage of surveys if they suffer from high rates of nonresponse, since post-survey adjustments for nonresponse require additional variables, the answer depends on the nature of the design and the quality of the additional variables.

Statistical estimates of multiple transcription factors binding in the model plant genomes based on ChIP-seq data

The development of high-throughput genomic sequencing coupled with chromatin immunoprecipitation technologies allows studying the binding sites of the protein transcription factors (TF) in the genome scale. The growth of data volume on the experimentally determined binding sites raises qualitatively new problems for the analysis of gene expression regulation, prediction of transcription factors target genes, and regulatory gene networks reconstruction. Genome regulation remains an insufficiently studied though plants have complex molecular regulatory mechanisms of gene expression and response to environmental stresses. It is important to develop new software tools for the analysis of the TF binding sites location and their clustering in the plant genomes, visualization, and the following statistical estimates. This study presents application of the analysis of multiple TF binding profiles in three evolutionarily distant model plant organisms. The construction and analysis of non-random ChIP-seq binding clusters of the different TFs in mammalian embryonic stem cells were discussed earlier using similar bioinformatics approaches. Such clusters of TF binding sites may indicate the gene regulatory regions, enhancers and gene transcription regulatory hubs. It can be used for analysis of the gene promoters as well as a background for transcription networks reconstruction. We discuss the statistical estimates of the TF binding sites clusters in the model plant genomes. The distributions of the number of different TFs per binding cluster follow same power law distribution for all the genomes studied. The binding clusters in Arabidopsis thaliana genome were discussed here in detail.

Vehicle Management and Emission Control and Maintenance

South Africa range 15th as the world largest CO2 emitter contributing to 1.2% of global emission. During the Kyoto Protocol of 2014, South Africa pledged to reduce its emission by 34% and 42% in 2020 and 2025 respectively. This study is a combination of literature review from South Africa with particular emphasis on road transport. The focus was on vehicle emission with reference to Limpopo Province to demonstrate how emissions from primarily the use of diesel and petrol as one of the major contributors to CO2 emission in the province are vital for the sustainability debate. The methodology used to illustrate the dangers of vehicular emissions were based on statistical estimates from the Department of Environmental Affairs (DEA) inventory report from 2000 to 2010. The information used in assessing the vehicle emission standards in Limpopo were obtained from DEA. The findings from literature reviews in general and the results from the field survey from Limpopo Province shed some light on South Africa's vehicle emissions policy issues and standards. Also the analysis focused on the impact of vehicular fleet management and carbon emissions. The article concludes by drilling down to vehicle users, motor vehicle repairs, engine over haulers, used engine collection and disposal with respect to their roles in vehicle emission and control in South Africa.

Numerical-statistical study of the prognostic efficiency of the SEIR model

A comparative analysis of the differential and the corresponding stochastic Poisson SEIR-models is performed for the test problem of COVID-19 epidemic in Novosibirsk modelling the period from March 23, 2020 to June 21, 2020 with the initial population N = 2 798 170. Varying the initial population in the form N = n m with m ⩾ 2, we show that the average numbers of identified sick patients is less (beginning from April 7, 2020) than the corresponding differential values by the quantity that does not differ statistically from C(t)/m, with C ≈ 27.3 on June 21, 2020. This relationship allows us to use the stochastic model for big population N. The practically useful ‘two sigma’ confidential interval for the time interval from June 1, 2020 to June 21, 2020 is about 108% (as to the statistical average) and involves the corresponding real statistical estimates. The influence of the introduction of delay on the prognosis, i.e., the incubation period corresponding to Poisson model is also studied.

Application of bayesian scientific approach to constructing the statistical estimations for solving metrological and measurement problems

Nowadays, constructing effective statistical estimates with a limited amount of statistical information constitutes a significant practical problem. The article is devoted to applying the Bayesian scientific approach to the construction of statistical estimates of the parameters of the laws of distribution of random variables. Five distribution laws are considered: The Poisson law, the exponential law, the uniform law, the Pareto law, and the ordinary law. The concept of distribution laws that conjugate with the observed population was introduced and used. It is shown that for considered distribution laws, the parameters of the laws themselves are random variables and obey the typical law, gamma law, gamma - normal law, and Pareto law. Recalculation formulas are obtained to refine the parameters of these laws, taking into account posterior information. If we apply the recalculation formulas several times in a row, we will get some convergent process. Based on a converging process, it is possible to design a process for self-learning a system or self-tuning a system. The developed scientific approach was applied to solve the measuring problems for the testing measuring devices and technical systems. The results of constructing point estimates and constructing interval estimates for these laws' parameters are given. The results of comparison with the corresponding statistical estimates constructed by the classical maximum likelihood method are presented.

Statistical Estimates of the Decline of the Russian Fertility: Regional Specifcs

The study focuses on analyzing regional features of the decline in the birth rate in Russia in 2016–2019. Taking into account regional specifcs is crucial when perfecting the implemented measures for improving the general demographic situation in the Russian Federation.The information base of the study contained time series of the total fertility rate in selected Russian regions. The author used methods of descriptive statistics and assessed convergent trends based on the sigma-, beta- and gamma-convergence methods. Spatial effects in regional differentiation of fertility were assessed based on Moran's I.As a result of the analysis, the following features were established. Firstly, in recent years in Russia, there has been a high degree of differentiation in the recorded declining birth rates. Secondly, the processes of falling fertility in the regions have specifc characteristics, the absence of typical trajectories in those subjects where it fell most or least of all. Thirdly, in Russia, there are no pronounced territo rial localizations of the processes of fertility decline. And fourthly, based on a comparison of the birth rate dynamics in Russian regions, no convergent trends have been identifed, i. e., there is no convergence of territorial entities in terms of the birth rate.According to the author, the demographic policy of recent years has not yet responded positively either in terms of birth rate growth or leveling of regional differences. The results obtained indicate that unifed approaches are unsuited to solving the demographic problems of Russian territories, and there is a need for demographic policy measures that take into account regional variability and are aimed at smoothing regional disproportions. Consequently, it is necessary to conduct regular statistical and demographic studies of the specificity of regional situations using methods of convergence and spatial autocorrelation analysis, rarely used in demography

Minimax model of transport operations of emergency on-orbit servicing in heliosynchronous orbits

Heliosynchronous orbits are attractive for space system construction. As a result, the number of spacecraft operating therein is constantly increasing. To increase their efficiency, timely on-orbit servicing (both scheduled and emergency) is needed. Emergency on-orbit servicing of spacecraft is needed in the case of unforeseen, emergency situations with them. According to available statistical estimates, emergency situations with serviced spacecraft are not frequent. Because of this, serviced spacecraft must be within the reach of a service spacecraft for a long time. In planning emergency on-orbit servicing, the following limitations must be met: the time it takes the service spacecraft to approach any of the serviced spacecraft must not exceed its allowable value, and the service spacecraft’s allowable energy consumption must not be exceeded. This paper addresses the problem of searching for emergency on-orbit servicing that would be allowable in terms of time and energy limitations and would meet technical and economical constraints. The aim of this work is to develop a mathematical constrained optimization model for phasing orbit parameter choice, whose use would allow one to minimize the maximum time of transport operations in emergency on-orbit servicing of a spacecraft group in the region of heliosynchronous orbits. The problem is solved by constrained minimax optimization. What is new is the formulation of a minimax (guaranteeing) criterion for choosing phasing orbit parameters that minimize the maximum time of emergency on-orbit servicing transport operations. In the minimax approach, the problem is formulated as the problem of searching for the best solution such that the result is certain to be attained for any allowable sets of indeterminate factors. The proposed mathematical model may be used in planning emergency on-orbit service operations to minimize the maximum duration of emergency on-orbit servicing transport operations due to a special choice of the service spacecraft phasing and parking orbit parameters.