Оценка рисков возможного превышения установленного времени ремонта объектов газотранспортной системы по малым выборкам
Prediction of the duration of a repair and maintenance project of a gas transport system is an important part of planning activities. There exist numerous sources of uncertainties that may result in time overruns possibly leading to multiple negative consequences. Our experience in planning this work suggests that accepting the stochastic nature of the project duration is a constructive step towards the preparedness to contingencies and defining penalties for repair companies. To support this approach, one needs to construct probability distributions of the durations of the projects. To address the issue of the scarcity of observed data, we suggest using a bootstrap resampling procedure. Gram-Charlier functions and order statistics are employed to approximate the distributions. It is demonstrated how to derive them for a separate repair project and a larger project consisting of a number of concurrently running subprojects. Following this, guidance is provided on how to decide about what duration should define the deadline for completion of the whole work. A simple example is provided.
The article presents the analysis of the measures of risk non-financial company. Identified key risk metrics. If justified the use of EVaR models. Developed methodical recommendations on the use of EVaR in stress-testing company.
Nowadays insurance market is one of the most rapidly developing sectors of economy, the purpose of which is to protect the property interests of individuals and legal entities under ensuing of specific events (insured accidents) at the expense of monetary funds formed from insurance dues (insurance premiums) paid by them. Probabilistic nature of insured accidents as well as the uncertainty of the moment of their occurrence and the severity of losses leads to the necessity of forming loss reserves. Reserves for incurred but not reported claims (hereinafter referred to as IBNR reserves) seem to be the most challenging in terms of actuarial calculations. The following article provides the descriptions of various actuarial techniques of loss reserving and examples of their application to a real insurance portfolio. In this paper the point estimating methods such as Chain Ladder, Bornhuetter-Fergusson, multiplicative techniques are compared with the stochastic method of Bootstrap and the most accurate estimate is determined using run-off analysis.
Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the main effects of distribution smoothness can be understood in terms of the ratio rho_12=(e_2 n_1)/(e_1 n_2), where e_1 and e_2 are the respective maximal lattice edge widths of the two populations, and n_1 and n_2 are the respective sample sizes used to compute the means. If rho_12 converges to an irrational number, or converges sufficiently slowly to a rational number; and in a number of other cases too, for example those where rho_12 does not converge; the effects of the discontinuity of lattice distributions are of smaller order than the effects of skewness. However, in other instances, for example where rho_12 converges relatively quickly to a rational number, the effects of discontinuity and skewness are of the same size. We also treat higher-order properties, arguing that cases where rho_12 converges to an algebraic irrational number can be less prone to suffer the effects of discontinuity than cases where the limiting irrational is transcendental. These results are extended to the case of three or more different means, and also to problems where distributions are estimated using the bootstrap. The results have practical interpretation in terms of the accuracy of inference for, among other quantities, the sum or difference of binomial proportions.ρ12=(e2n1)/(e1n2)e1e2n1n2ρ12ρ12ρ12ρ12
We introduce a new method for improving the coverage accuracy of confidence intervals for means of lattice distributions. The technique can be applied very generally to enhance existing approaches, although we consider it in greatest detail in the context of estimating a binomial proportion or a Poisson mean, where it is particularly effective. The method is motivated by a simple theoretical result, which shows that, by splitting the original sample of size n into two parts, of sizes n_1 and n_2=n-n_1, and basing the confidence procedure on the average of the means of these two subsamples, the highly oscillatory behaviour of coverage error, as a function of n, is largely removed. Perhaps surprisingly, this approach does not increase confidence interval width; usually the width is slightly reduced. Contrary to what might be expected, our new method performs well when it is used to modify confidence intervals based on existing techniques that already perform very well--it typically improves significantly their coverage accuracy. Each application of the split sample method to an existing confidence interval procedure results in a new technique.
This book presents recent non-asymptotic results for approximations in multivariate statistical analysis. The book is unique in its focus on results with the correct error structure for all the parameters involved. Firstly, it discusses the computable error bounds on correlation coefficients, MANOVA tests and discriminant functions studied in recent papers. It then introduces new areas of research in high-dimensional approximations for bootstrap procedures, Cornish–Fisher expansions, power-divergence statistics and approximations of statistics based on observations with random sample size. Lastly, it proposes a general approach for the construction of non-asymptotic bounds, providing relevant examples for several complicated statistics. It is a valuable resource for researchers with a basic understanding of multivariate statistics.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.