Probability Distributions Of Indices Research Articles

Exact and Explicit Probability Densities for One-Sided Lévy Stable Distributions

We study functions gα(x) which are one-sided, heavy-tailed Lévy stable probability distributions of index α, 0<α<1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expressions for gα(x), 0 ≤ x<∞, for all α=l/k<1, with k and l positive integers. We reproduce all the known results given by k ≤ 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a "fine-tuning" of α in order to adapt gα(x) to a given experimental situation.

A New Methodology for Probabilistic Short-Circuit Evaluation With Applications in Power Quality Analysis

The main aim of this paper is to propose a probabilistic short-circuit approach to generate the probability distributions of the System Average RMS Variation Index (SARFI) index. The proposed methodology is based on the combination of the admittance summation method in phase coordinates with the Monte Carlo method. This new approach has been tested in a feeder belonging to an electricity distribution company in the Northeast of Brazil to generate the probability distributions of the SARFI index. The tests results demonstrated that the proposed model is a powerful tool to stochastic prediction of voltage sags.

Predicting Bulk Electricity System Reliability Performance Indices Using Sequential Monte Carlo Simulation

System reliability performance is usually based on average customer interruption information. These average values are valuable information, but provide only a single customer risk dimension without underlying probability distributions. The average annual indices give no insight on how reliability may vary from year to year as a result of the random behavior of bulk electric systems (BES). A significant advantage when utilizing sequential Monte Carlo simulation in bulk electric system reliability analysis is the ability to provide reliability index probability distributions in addition to the expected values of their indices. Parameter distribution analysis and its potential utilization are relatively new concepts in composite power system reliability analysis and decision making. This paper presents a technique to predict future reliability performance indices of the BES using a sequential simulation approach. The results obtained using the sequential software show that the system performance index probability distributions have unique characteristics that are basically dependent on the system topology and the operating philosophy. Operating policies involving load shedding procedures have a considerable impact on the system performance indices and their associated distributions. Two test systems are used to illustrate the concepts associated with the determination of system performance indices and their associated probability distributions. The results obtained using two different load shedding policies are presented and compared.

Global observed changes in daily climate extremes of temperature and precipitation

A suite of climate change indices derived from daily temperature and precipitation data, with a primary focus on extreme events, were computed and analyzed. By setting an exact formula for each index and using specially designed software, analyses done in different countries have been combined seamlessly. This has enabled the presentation of the most up‐to‐date and comprehensive global picture of trends in extreme temperature and precipitation indices using results from a number of workshops held in data‐sparse regions and high‐quality station data supplied by numerous scientists world wide. Seasonal and annual indices for the period 1951–2003 were gridded. Trends in the gridded fields were computed and tested for statistical significance. Results showed widespread significant changes in temperature extremes associated with warming, especially for those indices derived from daily minimum temperature. Over 70% of the global land area sampled showed a significant decrease in the annual occurrence of cold nights and a significant increase in the annual occurrence of warm nights. Some regions experienced a more than doubling of these indices. This implies a positive shift in the distribution of daily minimum temperature throughout the globe. Daily maximum temperature indices showed similar changes but with smaller magnitudes. Precipitation changes showed a widespread and significant increase, but the changes are much less spatially coherent compared with temperature change. Probability distributions of indices derived from approximately 200 temperature and 600 precipitation stations, with near‐complete data for 1901–2003 and covering a very large region of the Northern Hemisphere midlatitudes (and parts of Australia for precipitation) were analyzed for the periods 1901–1950, 1951–1978 and 1979–2003. Results indicate a significant warming throughout the 20th century. Differences in temperature indices distributions are particularly pronounced between the most recent two periods and for those indices related to minimum temperature. An analysis of those indices for which seasonal time series are available shows that these changes occur for all seasons although they are generally least pronounced for September to November. Precipitation indices show a tendency toward wetter conditions throughout the 20th century.

Bulk Electric System Well-Being Analysis Using Sequential Monte Carlo Simulation

There is growing interest in combining deterministic considerations with probabilistic assessment in order to evaluate the "system well-being" of a composite generation and transmission system and to evaluate the likelihood not only of entering a complete failure state but also the likelihood of being very close to trouble. This paper presents bulk electric system well-being analysis using sequential Monte Carlo simulation. This approach provides accurate frequency and duration assessments and the index probability distributions associated with the mean values. The basic N-1 security criterion is used as the deterministic requirement for incorporating a deterministic consideration in a probabilistic assessment to monitor system well-being. The results shown in this paper indicate that the system well-being concept can provide comprehensive knowledge on what the degree of system vulnerability might be under a particular system condition. The basic concepts and their application in composite power system well-being analysis are illustrated by application to a small practical test system.

Delivery Point Reliability Indices of a Bulk Electric System Using Sequential Monte Carlo Simulation

A significant advantage when utilizing sequential Monte Carlo simulation in bulk electric system reliability analysis is the ability to provide reliability index probability distributions in addition to the expected values of their indices. Reliability index probability distributions provide a pictorial representation of the annual variability of these parameters around their mean values. Parameter distribution analysis and its potential utilization are relatively new concepts in composite power system reliability analysis and decision making. Computer software has been developed to produce reliability index probability distributions for the individual delivery points (DPs) in a bulk electric system. The results obtained using the sequential software show that the DP reliability index probability distributions have unique characteristics that are basically dependent on the system topology and the system operating philosophy. Operating policies such as load shedding procedures have a significant impact on the DP reliability indices and their associated distributions. The IEEE Reliability Test System is used to illustrate the concepts associated with the determination of DP and system indices and their associated probability distributions. The results obtained using two different load shedding policies are also presented and compared.

Analytical and Monte Carlo Approaches to Evaluate Probability Distributions of Interruption Duration

Regulatory authorities in many countries, in order to maintain an acceptable balance between appropriate customer service qualities and costs, are introducing a performance-based regulation. These regulations impose penalties-and, in some cases, rewards-that introduce a component of financial risk to an electric power utility due to the uncertainty associated with preserving a specific level of system reliability. In Brazil, for instance, one of the reliability indices receiving special attention by the utilities is the maximum continuous interruption duration (MCID) per customer. This parameter is responsible for the majority of penalties in many electric distribution utilities. This paper describes analytical and Monte Carlo simulation approaches to evaluate probability distributions of interruption duration indices. More emphasis will be given to the development of an analytical method to assess the probability distribution associated with the parameter MCID and the corresponding penalties. Case studies on a simple distribution network and on a real Brazilian distribution system are presented and discussed.

Incorporating Reliability Index Probability Distributions in Financial Risk Assessment with Performance Based Regulation

Regulatory authorities are increasingly adopting performance based regulations (PBR) in the new electric power utility environment. A PBR regime is intended to provide distribution utilities with economic incentives. It could also introduce potential financial risk due to the integration of a reward/penalty structure into the PBR plan. In this new environment, distribution utilities will need to adjust their reliability performance strategy to avoid possible financial risk, and could decide to invest in new capital projects to improve system reliability and be financially rewarded. This article illustrates the utilization of Monte Carlo simulation to develop the relevant reliability indices and their distributions due to reliability improvements in an electric distribution system. Quantitative consideration of the effect of system reliability improvements on the financial risk under imposed reward/penalty structures is presented. This work should be useful for electric power utilities working to reduce their risk and raise their profit in the new regulatory environment.

Historic Performance-Based Distribution System Risk Assessment

Regulatory authorities are increasingly adopting performance-based regulation (PBR) in the deregulated electricity industry. A PBR regime is intended to provide distribution utilities with incentives for economic efficiency gains. In order to discourage distribution utilities from sacrificing service reliability while pursuing economic incentives, historic utility performance is utilized as the specified service reliability standard in some places. A reward/penalty structure based on the historic reliability record could be integrated into a PBR plan. Historic reliability data are therefore, extremely important for distribution system risk assessment and remedial work in this new regime. This paper presents actual reliability data taken from the Canadian Electricity Association (CEA) Service Continuity Reports. The financial risk analyzes associated with the historic reliability data are conducted by incorporating reliability index probability distributions in imposed reward/penalty policies. The major cause contributions to the service continuity indices utilizing the CEA cause code categories are analyzed and illustrated. This work should prove useful for those utilities facing the emerging application of PBR.

Evaluation of the Probability Density Functions of Distribution System Reliability Indices With a Characteristic Functions-Based Approach

In reliability analysis of distribution systems, random events like the occurrence of a fault or the time to restore the service after a fault are represented by using random variables (RVs), so that the reliability indices built on the basis of these RVs also become RVs. Existing techniques for the evaluation of the probability distributions of reliability indices are typically based on Monte Carlo and analytical simulations. This paper presents a new method for computing the probability distribution of reliability indices. The random sums introduced by the randomness of the number of fault occurrences in the time interval of analysis are handled by using a characteristic functions-based approach. The direct convolution of the probability density functions is avoided by resorting to the properties of the compound Poisson process. In addition, the direct and inverse discrete Fourier transforms are used to allow for handling any type of probability distribution. The proposed method is an effective alternative to the existing methods, providing a fast and simple computation of probability distributions and moments for local and global reliability indices. Results obtained for large real urban distribution systems are presented.

Quantitative reliability considerations in the determination of performance-based rates and customer service disruption payments

The application of reliability index probability distributions to establish an appropriate balance between reliability improvement and cost saving strategies is discribed. Contracts between an administrative board and power utilities in the form of performance-based rates and contracts between a utility and a customer in the form of customer service disruption payments can be analysed using the appropriate index probability distributions. The developed concepts are illustrated using a test distribution system.

Evaluation of Probability Distributions of Distribution System Reliability Indices Considering WTG as Alternative Supply

Using wind turbine generators (WTG) as an alternative supply in a rural distribution system will affect both the mean values and the probability distributions of system reliability indices due to the fluctuating characteristics of wind speed. This paper investigates the impacts on the reliability indices and their probability distributions of using WTG as an alternative supply. A time sequential simulation technique is used to simulate the time-varying nature of wind speed and the random failure of system elements. The probability distributions of basic load point and system reliability indices for a modified rural distribution system are presented. The effects of WTG parameters on the index probability distributions are discussed.

Probability distribution of language lateralization indices in healthy subjects assessed by fTCD

Probability distribution of language lateralization indices in healthy subjects assessed by fTCD

Insights into Diversity and Niche Breadth Analyses from Exact Small-sample Tests of the Equal Abundance Hypothesis

-Exact test procedures are detailed for niche breadth as the general case, and for diversity as a subset of niche breadth analysis. Numerators of niche breadth probabilities are obtained as chain multiplications of three individually simple combinatorial calculations, only two of which are needed in analyses of species diversity. Algebraic checks on counts of terms and sums of numerators are developed. The two-niche case is used to demonstrate the high probabilities associated with high niche diversity, these effectively limiting tests for significant nonrandomness to the low diversity tail. Examination of diversity indices as rankordering devices reveals that all the common indices (Shannon's H', Brillouin's H, Simpson's C' and its close relatives) yield rank orders identical to some algebraic functions of the equiprobable 1:1:..:1 model, so that any use of these indices locks us into the equiprobable model no matter what alternative model we may claim as our intended interest. These common indices are found to yield very similar rank orderings, so that the likelihood of disagreement with a correct ordering is less than 5% for neighboring partitions of N organisms into n niches or s species, and much less than 5% for randomly selected partitions, even if a diversity index is selected at random without regard for its theoretical suitabilities. The statistical expectation of Simpson's C' (the complement of Simpson's original index) is found to be (n 1)/n for n niches regardless of N, and to be (s 1)/s for s species, to four decimal places or more, if species diversity sampling is continued until each species is represented on average by 7.5 individuals or more. The evenness measures V' and V, representing ratios of observed to maximum values of diversity indices, are found to attain values of 0.99 or more at the 50th percentiles of the probability distributions of diversity indices and are judged to be ecologically misleading and valueless. The claim that there is anything about Brillouin's H that suits it more to a census than a sample is disputed. Simpson's C' is recommended as the most serviceable of the examined indices, both because of the simple formulae for its statistical expectations and because its rank orderings are found to be identical to those given by the variance (or its square root) of the counts of species or niche occupants.

Evaluating the approximate probability distributions of load point reliability indices in power distribution networks

Evaluating the approximate probability distributions of load point reliability indices in power distribution networks

The behaviour of moisture adequacy index and its utilization for exploiting the agricultural potential in Punjab and Haryana

The moisture adequacy indices, the ratios of actual evapotranspiration to the potential evapotranspiration, have been found to follow closely the Beta distribution. The goodness of fit of the Beta distribution to the moisture index frequency distribution was tested using the Kolmogorov-Smirnov test for 144 station-months and 36 seasonal curves. 25 moisture adequacy curves failed the K-S tests. The probability distribution of moisture adequacy indices has been further used to assess irrigation requirement, optimum evapotranspiration, water management, land-use pattern and crop planning aspects for optimum utilization of available natural resources in the region.