Academic literature on the topic 'SIDS; binomial distribution'

The application of microgrids (MG) is more and more extensive, therefore it is important to improve the system management method of microgrids. The intended costs can be further minimized when the energy management system is unified with demand side response (DSR) strategies. In this work, we propose a generic method of modeling the equipment in a microgrid including multiple stochastic loads. The microgrid model can be generated on a computer by converting the energy circuit diagram into a signal flow diagram. Then, a demand side response method based on binomial distribution is introduced, and loads are set to different probabilities according to importance. By applying the probability of loads and changing the return coefficient of loads, the problem of individual differences in demand side responses is solved, so as to improve consumer satisfaction. The proposed model is constructed as a mixed-integer linear program (MILP). Cases studies demonstrate feasibility of the proposed modeling method. The demand side response achieves the expected goal. The system management method reduces the operation cost of the energy system of microgrids.

The linear regression model as well as the time series model is applied in many fields, in which the mean of the dependent variable is one function of the mean of the independent variables. However, to consider the regression model following in the Classical Statistics (the Frequent Statistics), it means that the parameters are the constants, in many situations, the regression model does not describe the fluctuation of both the dependent variable and the independent variables. Therefore, we need to modify the parameters following the random variable form, not the constant form, like as the regression in Bayesian Statistics. The other side, when the parameters considered as the random variables, computations in the regression model becomes very complex, because we need to compute the product of the probability distributions. So, we must evaluate about to vary of the variables' probability distributions not only the normal distribution, the Student distribution t, the Poisson distribution, the binomial distribution… In this paper, we estimated the dependent variable's probability distribution form through the simple Bayesian regression model in cases having many the probability distribution forms of the independent variable. In addition, we apply the results to real stock price data, proving that the most appropriate probability distribution with the data is a mixture of probability distributions, not a single normal distribution.

Fresno (Tolima), in Colombia, is a notable avocado producer, with 36% of the national production. In this paper, two sampling methods are presented to assess natural populations of Paraleyrodes Quaintance pos. bondari attacking avocado trees of Hass and Lorena cultivars under field conditions. The presence/absence of whitefly nymph colonies on 30 leaves located at the high, medium and low strata per host plant from both cultivars was evaluated. Visual estimations were performed to count the number ofwhitefly nymphs on 1.25 cm2 of five leaves/ bud in low and medium strata per tree to evaluate the spatial distribution of whitefly population in accordance to Poisson distribution, Negative Binomial distribution and b parameter of Law of Taylor. Significant differences in percentages of infestation (P≤0.03) from leaves that belonged to the low avocado tree strata were found between the Lorena (31.88±1.2%) and Hass (15.64±1.8%) cultivars. Natural populations of P. pos. bondari were located on the abaxial leaf side, showing an aggregate distribution in avocado tree from orchards located at different altitudes. Our findings recommend entomological surveillance for Paraleyrodes sp. pos. bondari in Fresno (Tolima), sampling four branches from the medium and low avocado tree strata through inspection of five buds/branches/tree throughout each branch with the presence/absence method to count whitefly nymph colonies on the abaxial side of pre-basal leaves. In total, the sampling involved five leaves/branch (20 leaves/strata or 40 leaves/tree) on 13 avocado trees per hectare.

A new class of distribution called the Fréchet binomial (FB) distribution is proposed. The new suggested model is very flexible because its probability density function can be unimodal, decreasing and skewed to the right. Furthermore, the hazard rate function can be increasing, decreasing, up-side-down and reversed-J form. Important mixture representations of the probability density function (pdf) and cumulative distribution function (cdf) are computed. Numerous sub-models of the FB distribution are explored. Numerous statistical and mathematical features of the FB distribution such as the quantile function (QUNF); moments (MO); incomplete MO (IMO); conditional MO (CMO); MO generating function (MOGF); probability weighted MO (PWMO); order statistics; and entropy are computed. When the life test is shortened at a certain time, acceptance sampling (ACS) plans for the new proposed distribution, FB distribution, are produced. The truncation time is supposed to be the median lifetime of the FB distribution multiplied by a set of parameters. The smallest sample size required ensures that the specified life test is obtained at a particular consumer’s risk. The numerical results for a particular consumer’s risk, FB distribution parameters and truncation time are generated. We discuss the method of maximum likelihood to estimate the model parameters. A simulation study was performed to assess the behavior of the estimates. Three real datasets are used to illustrate the importance and flexibility of the proposed model.

Let u,v∈N(u<v) and {T(x,y)=p^x q^y:x,y=u,u+1,u+2,u+3,…,v} be a string of sequence of success-failure events constituting the Bernoulli trials, with success p and failure q. Several probability distributions have derived their roots from the sequences of this form. However, it is our purpose to introduce new probability distribution functions that unify some of the existing ones generated by sets of this form mentioned in the literature and then give some of the statistics associated with it.

AbstractIn national birth registers of Caucasians, the secondary sex ratio, that is, the number of boys per 100 girls at birth, is almost constant at 106. Variations other than random variation have been noted, and attention is being paid to identifying presumptive influential factors. Studies of the influence of different factors have, however, yielded meagre results. An effective means of identifying discrepancies is to investigate birth data compiled into sibships of different sizes. Assuming no inter- or intra-maternal variations, the distributions of the sex composition are binomial. Varying parental tendencies for a specific sex result in discrepancies from the binomial distribution. Over a century ago, the German scientists Geissler and Lommatzsch analyzed the vital statistics of Saxony, including twin maternities, for the last quarter of the 19th century. They considered sibships ending with twin sets. Their hypothesis was that in sibships ending with male–male twin pairs, the sex ratio among previous births is higher than normal, while in sibships with female–female twin pairs, the sex ratio is lower than normal. If the sibship ended with a male-female pair, then the sex ratio is almost normal. Consequently, a same-sex twin set indicated, in general, deviations in the sex ratio among the sibs within the sibship. Our analyzes of their data yielded statistically significant results that support their statements.

Template attacks build a Gaussian multivariate model of the side-channel leakage signal generated by each value of a targeted intermediate variable. Combined with additional steps, such as dimensionality reduction, such models can help to infer a value with nearly 100% accuracy from just a single attack trace. We demonstrate this here by reconstructing the output of the binomial sampler of a Cortex-M4 imple- mentation of the Kyber768 post-quantum key-encapsulation mechanism. However, this performance is usually significantly diminished if the device, or even just the ad- dress space, used for profiling differs from the attacked one. Here we introduce a new technique for adapting templates generated from profiling devices in order to attack another device where we are also able to record many traces, but without knowledge of the random value held by the targeted variable. We interpret the model from the profiling devices as a Gaussian mixture and use the Expectation–Maximization (EM) algorithm to adapt its means and covariances to better match the unlabelled leakage distribution observed from the attacked setting. The Kyber binomial sampler turned out to be a particularly suitable target, for two reasons. Firstly, it generates a long sequence of values drawn from a small set, limiting the number of Gaussian components that need to be adjusted. Secondly, the length of this sequence requires particularly well-adapted templates to achieve a high key-recovery success rate from a single trace. We also introduce an extended point-of-interest selection method to improve linear discriminant analysis (LDA).

New formulas for the moments about zero of the Non-central Chi-Squared and the Non-central Beta distributions are achieved by means of novel approaches. The mixture representation of the former model and a new expansion of the ascending factorial of a binomial are the main ingredients of the first approach, whereas the second one hinges on an interesting relationship of conditional independence and a simple conditional density of the latter model. Then, a simulation study is carried out in order to pursue a twofold purpose: providing numerical validations of the derived moment formulas on one side and discussing the advantages of the new formulas over the existing ones on the other.

This paper provides an in-depth study on the impact of spare parts quality inspection on production costs in the electronics industry. By establishing a model based on binomial distribution, central limit theorem and right-hand side hypothesis testing, the costs, profits and losses of enterprises under different testing strategies are analysed. Firstly, for the inspection cost problem of accessory products, the minimum number of inspections is determined by assuming the number of sample defective products using binomial distribution and approximating the probability by De Moivre-Laplace theorem. Second, the simulated annealing algorithm is combined to derive 16 decision alternatives based on the analysis of control variables, and the best decision with the lowest total cost is finally determined. Finally, for the case of increasing number of spare parts and the appearance of semi-finished products, a mathematical model with minimising cost as the objective function is developed and solved using a genetic algorithm to evaluate the total cost under different inspection strategies. The study shows that the model proposed in this paper can reasonably solve the cost optimisation problem in electronic product quality inspection with high efficiency and practicality.

Epiphytic bryophytes are known to perform essential ecosystem functions, but their sensitivity to environmental quality and change makes their survival and development vulnerable to global changes, especially habitat loss in urban environments. Fortunately, extensive urban tree planting programs worldwide have had a positive effect on the colonization and development of epiphytic bryophytes. However, how epiphytic bryophytes occur and grow on planted trees remain poorly known, especially in urban environments. In the present study, we surveyed the distribution of epiphytic bryophytes on tree trunks in a Schima superba Gardn. et Champ. urban plantation and then developed count data models, including tree characteristics, stand characteristics, human disturbance, terrain factors, and microclimate to predict the drivers on epiphytic bryophyte recruitment. Different counting models (Poisson, Negative binomial, Zero-inflated Poisson, Zero-inflated negative binomial, Hurdle-Poisson, Hurdle-negative binomial) were compared for a data analysis to account for the zero-inflated data structure. Our results show that (i) the shaded side and base of tree trunks were the preferred locations for bryophytes to colonize in urban plantations, (ii) both hurdle models performed well in modeling epiphytic bryophyte recruitment, and (iii) both hurdle models showed that the tree height, diameter at breast height (DBH), leaf area index (LAI), and altitude (ALT) promoted the occurrence of epiphytic bryophytes, but the height under branch and interference intensity of human activities opposed the occurrence of epiphytic bryophytes. Specifically, DBH and LAI had positive effects on the species richness recruitment count; similarly, DBH and ALT had positive effects on the abundance recruitment count, but slope had a negative effect. To promote the occurrence and growth of epiphytic bryophytes in urban tree planting programs, we suggest that managers regulate suitable habitats by cultivating and protecting large trees, promoting canopy closure, and controlling human disturbance.

The renewable energy sources (RES) are intermittent in their nature and their integration in electric power grid has introduced the mismatch between supply and demand. This mismatch can be leveled by using the flexibilities from the supply and the demand side. The demand side in a power system has key importance in the evolving context of the energy systems. Electrical load patterns that represent the consumption level are affected by different types of uncertainties associated with customer’s behavior and with keeping acceptable comfort level. The resulting aggregated load pattern indicates the system response that may be more or less flexible in different periods of time. The distribution system operator in a microgrid is responsible for its secure and economic operation. Enhancing the knowledge on the aggregated behavior of these customers is particularly important for the distribution system operator, also with the aim of determining the potential flexibility of the demand and setting up the economic terms of the electricity provision to the customers. Extra charges due to high energy demand and contract violation penalties can be avoided using demand side flexibility. Demand side flexibility has many benefits in normal as well as emergency conditions like less cost and quick response. The study of aggregate residential demand for flexibility measures is important due to the diverse energy usage behavior of individual residents and conceptually, its availability all around the year for load management. Exploitation of possible flexibilities of the group of residential customer’s behavior is considered as an important option to promote demand response programs and to achieve greater energy savings. As far as the residential sector is concerned, a reasonable work can be found in the literature to assess the flexibility for the individual appliances, the aggregation of selected appliances. However, little work is found on the aggregation of residential units. Also, despite of many discussions about the concept of flexibility, the few mathematical definitions of flexibility available do not address the variation in time of the overall demand aggregation. There is a need to develop a methodology to extract flexibility information from aggregate electricity consumption behavior of the residents and develop useful flexibility indices for the aggregate residential loads. For this purpose, the first action required is to augment availability of information about the characteristics of aggregate electricity demand. The analysis of aggregate demand patterns is carried out by considering the demand pattern data representing the average power determined from the energy referring to a given time step duration. This thesis contains a comprehensive statistical analysis to investigate the effect of time step duration and aggregation level on load variation profile. Then the customer behavior about the change is demand is modeled using the binomial probability distribution. This model has led towards some novel definitions of flexibility indices. A new method based on the Beta probability distribution has been developed to generate the time coupled aggregate residential demand patterns, whose evolution depends on the uncertainties associated with the customer’s behavior. The outcome of this research work has also led towards defining the role of customers in microgrid application. For this purpose, a structure of the business model for a smart (mini) grid is proposed. The data sets used for all kind of analysis are generated for the different aggregations of the extra-urban residential customers using a bottom-up approach. The tools presented in this research work can be helpful for a system operator or an aggregator to assess demand side flexibilities, manage resources and efficiently use demand response programs. The findings of this work are also supportive to determine the metering structure for a microgrid application in which, by using current ICT technologies, it is possible to decide a compromise solution between the aggregation level and time step duration for smart metering. On the other hand, the research findings also led to the conclusion that the flexibility level for the individual residential customers is not so high to give economic benefits that make it attractive to participate in DR programs. From the studies, it seems that the problem is not with the technical aspects but with the current business model of the smart grids. For the future extension of this work, a framework of a new smart business model for smart (mini) grids, centric to customers, is presented. It is expected that the developments using the proposed background of the business model can lead towards a different era in the development of the power systems with the new wave of research; as new tools are required to embed economic and social considerations in planning the proposed architecture.

Bayes methods in statistical inference are one of the important methods, and most of the research and messages tend to use the Bayes method in the estimation process. The regular Bayes method does not meet this problem, so in this thesis it is possible to verify the existence of prior data conflict by modeling the parameters of the prior distribution and then comparing the standard deviation of the prior distribution with the standard deviation of the posterior distribution, if the value of the standard deviation of the prior distribution is greater than the deviation. The standard distribution for the posterior distribution, it means that there is a problem of prior data conflict. Then we used an approach to solve this problem through a set of prior distributions called this approach by the robust Bayesian method, to identify the behavior of the estimators, two types of failure models were used, the first Weibull distribution to match it with continuous data. The second is a (Binomial) distribution to match the discrete data, the regular Bayes method is compared with the robust Bayesian method by using integrated mean square error (IMSE). In the Weibull distribution, the scale parameter (θ) and the survival function were estimated for two simulation experiments, the first was in the case of prior data unconflict the second was in the case of prior data conflict, so the simulation results showed that the robust Bayes method is the best by using the comparison criterion integrated mean square error (IMSE). On the practical side, real data were collected from Al-Manathira Hospital of the Najaf Health Department for the deaths of heart attack patients for 2018, the time of admission of the patient to the hospital until death was recorded, which is the time Exit where a sample of (15) patients was collected and the test of goodness of fit showed that the data follow a Weibull distribution with two parameters, the robust Bayes method was used to estimate the scale parameter and the survival function. As for the Binomial distribution, the parameter (P) and survival function were estimated for two experiments from the first simulation, which was in the case of prior data unconflict, as for the second experiment, it was in the case of prior data conflict. The simulation results showed that the robust Bayes method is the best by using the comparison criterion (IMSE). On the practical side, real data were collected from Yarmouk Teaching Hospital on breast cancer patients’ mortality from 2010 to 2017, and the test of goodness of fit showed that the data follow a Binomial distribution, the robust Bayes method was used to estimate the parameter (P) and survival function.