Well-known Distribution Research Articles

Gram–Charlier-Like Expansions of the Convoluted Hyperbolic-Secant Density

Since financial series are usually heavy tailed and skewed, research has formerly considered well-known leptokurtic distributions to model these series and, recently, has focused on the technique of adjusting the moments of a probability law by using its orthogonal polynomials. This paper combines these approaches by modifying the moments of the convoluted hyperbolic secant. The resulting density is a Gram–Charlier-like (GC-like) expansion capable to account for skewness and excess kurtosis. Multivariate extensions of these expansions are obtained on an argument using spherical distributions. Both the univariate and multivariate (GC-like) expansions prove to be effective in modeling heavy-tailed series and computing risk measures.

Detector-Agnostic Phase-Space Distributions.

The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of well-known phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single- and two-photon states in phase space and certify their nonclassicality with high statistical significance.

Thompson Sampling-Based Channel Selection Through Density Estimation Aided by Stochastic Geometry

We propose a sophisticated channel selection scheme based on multi-armed bandits and stochastic geometry analysis. In the proposed scheme, a typical user attempts to estimate the density of active interferers for every channel via the repeated observations of signal-to-interference power ratio (SIR), which demonstrates the randomness induced by randomized interference sources and fading effects. The purpose of this study involves enabling a typical user to identify the channel with the lowest density of active interferers while considering the communication quality during exploration. To resolve the trade-off between obtaining more observations on uncertain channels and using a channel that appears better, we employ a bandit algorithm called Thompson sampling (TS), which is known for its empirical effectiveness. We consider two ideas to enhance TS. First, noticing that the SIR distribution derived through stochastic geometry is useful for updating the posterior distribution of the density, we propose incorporating the SIR distribution into TS to estimate the density of active interferers. Second, TS requires sampling from the posterior distribution of the density for each channel, while it is significantly more complicated for the posterior distribution of the density to generate samples than well-known distribution. The results indicate that this type of sampling process is achieved via the Markov chain Monte Carlo method (MCMC). The simulation results indicate that the proposed method enables a typical user to determine the channel with the lowest density more efficiently than the TS without density estimation aided by stochastic geometry, and $\epsilon $ -greedy strategies.

Assessment of Wind Power Potential at Eastern-Jerusalem, Palestine

Due to the energy demand and lack of supplied energy of Palestinian cities, wind resource assessment is important and necessary. The objective of the work is to analyze the wind speed data characteristics and wind power potential at eastern Jerusalem that are collected at 10 m above ground level from 2008 to 2018. The variations of monthly, seasonal, and annual wind speed are analyzed, and the measured maximum, minimum, and mean values are presented in this study. Wind speed characteristics have been analyzed by the well-known Weibull distribution function, and used to evaluate the wind power of the proposed site. Moreover, the relationship between wind power and mean wind speed is fitted by a second-order polynomial. The shape parameter moderate values showed that wind speed was relatively steady at the site. The highest average maximum value was found to be 5.7 m/s in June-2008, whereas the mean maximum values ranged from 5.4 m/s in June to 3.8 m/s in November. The highest mean power value was found to be 31.66 w/m2 in July with a maximum value of 23.18 w/m2 in 2013. R2 of the polynomial fit provides values of 95% for monthly mean and 96% for annual mean.

Unified analysis of channel capacity under different adaptive transmission policies

In this Letter, the channel capacity under different transmission policies is analysed using a mixture gamma distribution. Specifically, the capacity of the channel with inversion and fixed rate, optimum power and rate adaptation, and truncated inversion and fixed rate IS derived in unified exact simple closed-form expressions. The composite α − λ − η − μ /gamma fading channel which includes most of the well-known fading distributions as special cases, has been employed in this work. Moreover, a comparison between numerical and simulation results has been carried out to verify the validation of the derived expressions.

Modelling Insurance Losses with a New Family of Heavy-Tailed Distributions

The actuaries always look for heavy-tailed distributions to model data relevant to business and actuarial risk issues. In this article, we introduce a new class of heavy-tailed distributions useful for modeling data in financial sciences. A specific sub-model form of our suggested family, named as a new extended heavy-tailed Weibull distribution is examined in detail. Some basic characterizations, including quantile function and raw moments have been derived. The estimates of the unknown parameters of the new model are obtained via the maximum likelihood estimation method. To judge the performance of the maximum likelihood estimators, a simulation analysis is performed in detail. Furthermore, some important actuarial measures such as value at risk and tail value at risk are also computed. A simulation study based on these actuarial measures is conducted to exhibit empirically that the proposed model is heavy-tailed. The usefulness of the proposed family is illustrated by means of an application to a heavy-tailed insurance loss data set. The practical application shows that the proposed model is more flexible and efficient than the other six competing models including (i) the two-parameter models Weibull, Lomax and Burr-XII distributions (ii) the three-parameter distributions Marshall-Olkin Weibull and exponentiated Weibull distributions, and (iii) a well-known four-parameter Kumaraswamy Weibull distribution.

AREA OF P-N JUNCTION WITH THE TUNNEL BREAKDOWN MECHANISM AS A FACTOR IN THE DESIGN OF SEMICONDUCTOR DEVICES

This article presents the results of an experimental study on the influence ofp-n junction area (Sp.„) on the breakdown voltage (Ubr) of low-voltage p-n structures with avalanche, mixed and tunnel breakdown mechanisms. The nature and behaviour of the experimentally obtained Ubr(Sp.„) curves fully correspond to the well-known distribution ofp-n junction curves by the type of an electric breakdown. 'For Ubr > 6.7 V, the avalanche breakdown voltage ofp-n junctions remains unchanged over a wide range ofSp.„ values. Below ~6. 7 V, in the region of mixed breakdown ~(6.7 - 4.7) V, Ubr decreases with an increase of Sp-n for fixed values ofpr. Moreover, for pr (0.007 ^ 0.001) Ohms cm, in the region of the tunnel breaksdown mechanism (Ubr <4.7 V), , Ubr(Sp.„J curve shows non-linear behaviou. The effect of non-linear dependence between Ubr and (Sp.„.t) for p-n junctions with tunnel breakdown is used in the designs of low-voltage Zener diodes and voltage regidators with Ust7 Ubr less than 5 V. The dependence between Ubr.t and (Sp-„.t) for p-n structures with tunnel breakdown can be used in designing novel voltage converters with negative resistance. In particidar, this article shows the implemented experimental design of a voltage converter based on two p+-n+junctions with breakdown voltages of ~4.3 V.cmd ~2.3 V. based on p-type silicon w ith a specific resistance of 20 Ohms cm, controlled by a MOSFET, system.

Assessment of Flight Block Time Reliability Under Different Delay Time Windows: A Case Study

In transportation field, reliability is the probability of reaching the destination from the starting point within the expected time. While the concept of reliability, including travel time reliability model and its evaluation indicators have been extensively studied in ground transportation, they are relatively very scarce in air transportation. Flight block time reliability not only exert a strong influence on passenger behavior but also greatly affect aerodromes, airlines and air traffic management, thus affecting the entire air transportation. This paper proposes a methodology for evaluating the flight block time under different delay time windows. We applied the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) method to set windows which reflects different delays. We proposed a probabilistic model of flight block time based on a series system. A case study is performed to compare flight block time, flight air time, flight taxi-in time, and flight taxi-out time at different time reliability metrics with different delays. In particular, we found the best fit for each flight time segment of three delay time windows among nine well-known distribution functions to calculate the flight block time reliability indexes. Based on our analysis, we find that the reliability of delay time window 3 from 22:20- 23:00 to be relatively less compared to the other delay time windows. The results from the reliability estimation demonstrate that the model is efficient in estimating the reliability of flight block time in different delay time windows.

A non-Hermitian quantum approach to reliability of a two-state system

We explore the concept of the reliability theory in the quantum domain, by giving a Hilbert structure to the system states, then utilize a non-Hermitian Schrodinger equation to describe the state evolution and finally derive two new lifetime distributions. Beyond this, the alternative density matrix approach implies that the degradation term can be separated into two parts, one only related to the system properties and the other only influenced by the environment. Applications on six real data sets further show that the proposed models can outperform the existing well-known distributions, which verifies the validity of the proposed method.

On the Reliability for Some Bivariate Dependent Beta and Kumaraswamy Distributions: A Brief Survey

Abstract In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability {R=\Pr(X<Y)} . The algebraic form for {R=\Pr(X<Y)} has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when {(X,Y)} follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution are dependent bivariate beta and bivariate Kumaraswamy. The calculations involve the use of special functions.

A Modified Negative Binomial Distribution: Properties, Overdispersion and Underdispersion

In this paper, we introduce a new and useful discrete distribution (modified negative binomial distribution) and its statistical and probabilistic properties are discussed. This distribution is a three-parameter extension of the negative binomial distribution that generalizes some well-known discrete distributions (negative binomial and geometric). Various statistical and probabilistic properties were derived such as moments, probability and moment generating functions and maximum likelihood estimation of parameters. Modified negative binomial distribution is appealing from a theoretical point of view since it belongs to the exponential family as well as to the weighted negative binomial distributions family. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. Finally, a real numerical example is also considered for illustrative purpose.

Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications

In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics.

Tsallis–Mittag-Leffler distribution and its applications in gas prices

The theory of Mittag-Leffler process is a fundamental concept in probability and stochastic process. This paper introduces the class of Tsallis–Mittag-Leffler distributions. In special case, our results include a new Tsallis q-Weibull distribution, one-parametric Mittag-Leffler distribution and some other well-known distributions. Finally, to illustrate the applicability of our distribution, a real data set on gas prices in time series data based on 100 days moving average is analyzed.

Reliability Evaluation of Compacted Tropical Red Soil Admixed with Waste Wood Ash for Use as Road Construction Material

A first-order reliability program (FORM) was applied to evaluate the potential of Tropical Red Soil (lateritic soil) admixed with waste wood ash (WWA) and compacted with British Standard Light (BSL) energy for use as road construction material. Regression models were developed from laboratory data using Mini-tab R15 software which served as limit state equations for the reliability analysis. Using the developed models for compaction characteristics, and a well-known distributions for the related soil parameters, safety indices were calculated considering compaction characteristics (maximum dry density, MDD and optimum moisture content, OMC) as dependent variables and the soil parameters (content of WWA, content of clay, content of silt, content of sand and specific gravity as independent variables). The results revealed that safety index is influenced by alteration in the soil parameters. Results shows that content of clay, content of silt, content of sand and specific gravity are significantly affected by the change in coefficient of variation (COV) and for that reason must be firmly controlled in lateritic soil-waste wood ash (WWA) mixtures compacted with BSL energy for use in road pavement as sub-base material. It was evident from the safety index that WWA content has little effect as its value almost continued unchanged at all COV values used. Stochastically, the BSL energy used did not yield satisfactory safety index value of 1.0 as recommended by the Nordic Committee on Building Regulation. Hence, higher energy level with better additives having higher potency such as cement, lime or bitumen is suggested to model compaction characteristics of lateritic soil-waste wood ash (WWA) mixtures for road pavement purpose as sub-base material for 10-100% variation in COV.

On Generalized Linear Exponential Distribution: Different Methods of Estimation

This paper concerns with various techniques for estimations from the generalized linear exponential distribution (GLED) that can be used for modeling bathtub, increasing and decreasing hazard rate (HR) behavior and was first proposed by [3]. This distribution is important since it contains as special sub-models some widely well-known distributions such as the exponential distribution (ED), the Rayleigh distribution (RD), the linear exponential distribution (LED), and the Weibull distribution (WD). The various techniques for estimations can be considered as maximum likelihood estimation (MLE), least-square estimation (LSE), weighted least square estimation (WLSE), Cramer Von-Mises estimation (CVME), and Anderson Darling estimation (ADE). These methods of estimations are used to estimate the unknown parameters of the well-known GLED. Two applications are used to show that the GLED is a viable distribution in modeling lifetime data and to compare the varying methods of estimations based on the Kolmogorov-Simnorov test with the corresponding P-value to show the optimal method. Finally, a simulation study is presented to compare the varying methods of estimation based on the mean square error (MSE) and the average absolute bias (AAB).

Car Speed Distribution in Front of a Stop-Line of Urban Regulated Intersection

Problem. Car speed is a very important indicator of the traffic organization level in conditions of the formed street-road network. The car speed in a particular place and at a specific time is definitely random, and therefore should be described by the distribution law. The generally well-known normal distribution of the car speed in free traffic conditions is transformed into another distribution when these conditions complicate. The strictest conditions are those where the car is forced to stop completely and stand for some time in anticipation of permission for further movement. One such case is regulated intersections, and therefore the establishment of a car speed distribution in these conditions is an urgent task for which a new concept of a car speed should be introduced. Goal. The goal is testing the hypothesis about the possibility of describing the car speed fluctuations in front of the stop-line of a regulated intersection by an exponential distribution law. Methodology. Development of the method for the car speed measuring in front of the stop-line of the city regulated intersection on the basis of understanding the speed as the average speed of a car passing distance through the road cross-section. Results. The results of observing the actual speed at a regulated intersection lead to the conclusion that a regulated intersection can significantly complicate the traffic conditions in comparison with the narrow passageway and this is reflected in the decrease of the average speed of vehicles and the growth of its standard deviation, that brings the gamma-distribution close to the exponential form. Originality. A new method of a car speed estimating was proposed, on the basis of which the method was developed and the hypothesis was tested regarding the indicator distribution of the car speed in front of the stop-line of the regulated intersection. Practical value. The obtained result allows to increase accuracy of the car speed prediction in analytical and simulation models of transport network functioning.

A Resilience-Based Architecture for Joint Distributed Energy Resources Allocation and Hourly Network Reconfiguration

As a result of the recent innovations in the deployment of plug-in electric vehicles (PEVs), this technology can play an important role as a distributed energy resource in supplying the system demand of the power systems of the future. This paper introduces a methodology for optimal coordinated allocation of wind farms (WFs), energy storage systems, and PEV's parking lots considering demand response programs and hourly distribution network reconfiguration in normal and severe contingency conditions. In the proposed methodology, the participation of different types of loads is also examined. The objective function is to minimize the total costs of purchased power from the upstream network and WFs, along with the costs of commercial/industrial loads flexibility and residential loads curtailment. To validate the performance of the proposed methodology, it is implemented on the well-known IEEE 33-bus distribution test system. The simulation results validate the feasibility and effectiveness of the proposed approach.

A new extended generalized Gompertz distribution with statistical properties and simulations

Statistical distributions are very useful in describing and predicting real world phenomena. In many applied areas there is a clear need for the extended forms of the well-known distributions. Generally, the new distributions are more flexible to model real data that present a high degree of skewness and kurtosis. The choice of the best-suited statistical distribution for modeling data is very important.In this article, we proposed an extended generalized Gompertz (EGGo) family of EGGo. Certain statistical properties of EGGo family including distribution shapes, hazard function, skewness, limit behavior, moments and order statistics are discussed. The flexibility of this family is assessed by its application to real data sets and comparison with other competing distributions. The maximum likelihood equations for estimating the parameters based on real data are given. The performances of the estimators such as maximum likelihood estimators, least squares estimators, weighted least squares estimators, Cramer-von-Mises estimators, Anderson-Darling estimators and right tailed Anderson-Darling estimators are discussed. The likelihood ratio test is derived to illustrate that the EGGo distribution is better than other nested models in fitting data set or not. We use R software for simulation in order to perform applications and test the validity of this model.

Echinoids from the Tesero Member (Werfen Formation) of the Dolomites (Italy): implications for extinction and survival of echinoids in the aftermath of the end-Permian mass extinction.

The end-Permian mass extinction (∼252 Ma) was responsible for high rates of extinction and evolutionary bottlenecks in a number of animal groups. Echinoids, or sea urchins, were no exception, and the Permian to Triassic represents one of the most significant intervals of time in their macroevolutionary history. The extinction event was responsible for significant turnover, with the Permian–Triassic representing the transition from stem group echinoid-dominated faunas in the Palaeozoic to Mesozoic faunas dominated by crown group echinoids. This turnover is well-known, however, the environmental and taxonomic distribution of echinoids during the latest Permian and Early Triassic is not. Here we report on an echinoid fauna from the Tesero Member, Werfen Formation (latest Permian to Early Triassic) of the Dolomites (northern Italy). The fauna is largely known from disarticulated ossicles, but consists of both stem group taxa, and a new species of crown group echinoid, Eotiaris teseroensis n. sp. That these stem group echinoids were present in the Tesero Member indicates that stem group echinoids did not go extinct in the Dolomites coincident with the onset of extinction, further supporting other recent work indicating that stem group echinoids survived the end-Permian extinction. Furthermore, the presence of Eotiaris across a number of differing palaeoenvironments in the Early Triassic may have had implications for the survival of cidaroid echinoids during the extinction event.

The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates

ABSTRACTThe Beta distribution is the standard model for quantifying the influence of covariates on the mean of a response variable on the unit interval. However, this well-known distribution is no longer useful when we are interested in quantifying the influence of such covariates on the quantiles of the response variable. Unlike Beta, the Kumaraswamy distribution has a closed-form expression for its quantile and can be useful for the modeling of quantiles in the absence/presence of covariates. As an alternative to the Kumaraswamy distribution for the modeling of quantiles, in this paper the unit-Weibull distribution was considered. This distribution was obtained by the transformation of a random variable with Weibull distribution. The same transformation applied to a random variable with Exponentiated Exponential distribution generates the Kumaraswamy distribution. The suitability of our proposal was demonstrated to model quantiles, conditional on covariates, with two simulated examples and three real applications with datasets from health, accounting and social science. For such data sets, the obtained fits of the proposed regression model were compared with those provided by the Beta and Kumaraswamy regression models.