Well-known Distribution Research Articles

Deviations from Poisson statistics in the spectra of free rectangular thin plates.

The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency levels belonging to different symmetry classes cross each other and (ii) for levels within the same symmetry sector, only avoided crossings appear. The consequence of anticrossings is studied by calculating the distribution of the ratio of consecutive level spacings for each symmetry class. The resulting ratio distributions disagree with the expected Poissonian result. They are then compared with some well-known transition distributions between Poisson and the Gaussian orthogonal random matrix ensemble. It is found that the distribution of the ratio of consecutive level spacings agrees with the prediction of the Rosenzweig-Porter model. Also, the normal-mode vibration amplitudes are found experimentally on aluminum plates, before and after an avoided crossing for symmetrical-symmetrical, symmetrical-antisymmetrical, and antisymmetrical-symmetrical classes. The measured modes show an excellent agreement with our numerical predictions. The expected Poissonian distribution is recovered for the simply supported rectangular plate.

Estimating duration distribution aided by auxiliary longitudinal measures in presence of missing time origin.

Understanding the distribution of an event duration time is essential in many studies. The exact time to the event is often unavailable, and thus so is the full event duration. By linking relevant longitudinal measures to the event duration, we propose to estimate the duration distribution via the first-hitting-time model (e.g. Lee and Whitmore in Stat Sci 21(4):501–513, 2006). The longitudinal measures are assumed to follow a Wiener process with random drift. We apply a variant of the MCEM algorithm to compute likelihood-based estimators of the parameters in the longitudinal process model. This allows us to adapt the well-known empirical distribution function to estimate the duration distribution in the presence of missing time origin. Estimators with smooth realizations can then be obtained by conventional smoothing techniques. We establish the consistency and weak convergence of the proposed distribution estimator and present its variance estimation. We use a collection of wildland fire records from Alberta, Canada to motivate and illustrate the proposed approach. The finite-sample performance of the proposed estimator is examined by simulation. Viewing the available data as interval-censored times, we show that the proposed estimator can be more efficient than the well-established Turnbull estimator, an alternative that is often applied in such situations. Supplementary InformationThe online version contains supplementary material available at 10.1007/s10985-021-09520-w.

NAIVE STATISTICAL ANALYSES FOR COVID-19: APPLICATION TO DATA FROM BRAZIL AND ITALY

This article is a direct consequence of the authors' desire to discuss the role of statistics in data analysis. The analysis of coronavirus (COVID-19) databases are used as to show simple, but powerful statistical frameworks. We do believe that models for assessing future trends in temporal data in general, and in cases and/or deaths of COVID-19, belongs to the area of (Bio)Statistics. Just as engineers use knowledge of physics, chemistry and often architecture, when constructing bridges, buildings and roads, statisticians use knowledge of mathematics, computer science and even physics for modelling, analysing, and forecasting in order to transform data into information. While the statistician's contribution is rarely acknowledged, everyone knows that a building is a work of an engineer. Nonetheless, nowadays statistics has been gaining the attention that it deserves due to the rise of big data and data science that was built on the foundationsof statistics. This article shows that, even with only basic knowledge of statistics, one can adequately collaborate with the community in dealing with very important issues such as the COVID-19 numbers. In order to model and to obtain predictions we use well-known distributions to statisticians working on survival analysis: gamma, Weibull and log-normal distributions. We also make use of singular spectrum analysis, a simple non-parametric time series methodology, for an analogous purpose. Survival analysis is a research area widely used in Biostatistics and even in Reliability, while time series analysis is widely used across areas where the data is measured along the time.

Empirical Models for NB-IoT Path Loss in an Urban Scenario

The lack of publicly available large-scale measurements has hindered the derivation of empirical path-loss (PL) models for Narrowband Internet of Things (NB-IoT). Therefore, simulation-based investigations currently rely on models conceived for other cellular technologies, which are characterized, however, by different available bandwidth, carrier frequency, and infrastructure deployment, among others. In this article, we take advantage of data from a large-scale measurement campaign in the city of Oslo, Norway, to provide the first empirical characterization of NB-IoT PL in an urban scenario. For the PL average term, we characterize Alpha-Beta-Gamma (ABG) and Close-In (CI) models. By analyzing multiple NB-IoT cells, we propose a statistical PL characterization, i.e., the model parameters are not set to a single constant value across cells, but are randomly extracted from well-known distributions. Similarly, we define the PL shadowing distribution, correlation over distance, and intersite correlation. Finally, we give initial insights on the outdoor-to-indoor propagation, using measurements up to deep indoor scenarios. The proposed models improve the PL estimation accuracy compared to the ones currently adopted in NB-IoT investigations, enabling more realistic simulations of urban scenarios similar to the sites covered by our measurements.

Optimal probabilistic location of DGs using Monte Carlo simulation based different bio-inspired algorithms

Stochastic nature of load demand has a great impact on the performance of electrical power system. As a result, planning of electrical power system considering load uncertainties became inevitable. This paper presents Monte Carlo simulation based different bio-inspired algorithms, grey wolf optimization (GWO), manta ray foraging optimization (MRFO), satin bower bird optimization (SBO) and whale optimization (WOA) to optimize locations of three DG units under load uncertainties considering 500 scenarios. Each scenario includes 50 iterations which means that for each run we have 25,000 iterations and 500 characteristics for different load value. Two objectives are achieved. Firstly, statistically finding the optimal probabilistic location of three DG units under load uncertainties in IEEE 33-bus and IEEE 69-bus radial distribution system based on Monte Carlo simulation integrated with different bio-inspired algorithms. Secondly, comparing between the performances of four different bio-inspired algorithms. Three objective functions are considered, minimizing active power loss, minimizing voltage deviation and maximizing voltage stability index. The active and reactive power demand are normally distributed using normal distribution function. The optimal probabilistic location is investigated considering two cases under load uncertainties, optimizing location of three DG units generally and optimizing location of one DG unit assuming two optimum locations for the other two units extracted from case I. The obtained results (after placing DG units) are compared to the base case (DG units are not connected) and compared to each other according to the optimization technique. The results show that, SBO algorithm superiors other algorithms almost in all cases. Comes next GWO which provide good results generally. However, the good performance obtained by MRFO, it consumes twice the time of other algorithms. WOA however fast convergence, it provides results worse than other algorithms. The system is applied to the well-known IEEE 33-bus and IEEE 69-bus radial distribution system.

Does Reproducibility Drive Clinical Accuracy?

To develop a stochastic model relating measurement uncertainty, including reproducibility, to clinical accuracy, as demonstrated by the receiver operating characteristic curve. A model is developed based on the symmetric case of the well-known binormal distribution. The overall distribution is partitioned further into analytical and biological components based on assumptions derived from the Cotlove criterion. Explicit mathematical solutions are derived and further verified by Monte Carlo analyses. The model demonstrates that tests with analytical error that conforms to the classic Cotlove criterion can achieve receiver operating characteristic curves with areas under the curve of 0.68 to 0.76 and Youden indices of 0.26 to 0.38 but have overall agreement for duplicate measurements of only 80% to 82%. Furthermore, the analytically accurate agreement is only 75% to 78%, and the clinically accurate agreement is only 50% to 60%. The model suggests that assays may have reasonable clinical accuracy despite having reproducibility of less than 85%. Imperfect assays can substantially improve medical decision-making. The findings must be interpreted with caution given the binormal assumptions, but such assumptions are often useful as a first approximation. Practicing pathologists should feel comfortable performing semiquantitative assays shown to have a strong biological association with clinical outcome.

Performance rating of the Zubair Gompertz distribution : Properties and applications

Real world scenarios have been described using statistical distributions. Often these distributions extend the well-known distributions in efficiency and flexibility. This article introduces a new class of distribution called Zubair Gompertz (ZUG) distribution. The proposed model has a hazard shaped that is decreasing, unimodal, left skewed, and increasing. Some statistical properties of the proposed distribution were presented and investigated. The ZUG model is expressed as a linear function of the Gompertz densities. The maximum likelihood method was used to obtain the parameters of the proposed distribution. The performance of the ZUG model was illustrated by application to real-life data sets. The results show that the ZUG density provides a better goodness-of-fit in terms of their test statistic and would serve as a better alternative model in statistical literature.

Query expansion based on term distribution and DBpedia features

Query Expansion (QE) approaches that involve the reformulation of queries by adding new terms to the initial user query, are intended to ameliorate the vocabulary mismatch between the query keywords and the documents’ in Information Retrieval Systems (IRS). One big issue in QE is the selection of the right candidate terms for expansion. For this purpose Linked Data can be used, as a valuable resource, for providing additional expansion features such as the values of sub- and super classes of resources. The underlying research question is whether interlinked data and vocabulary items provide features which can be taken into account for query expansion. In this paper, we introduced a new QE approach that aimed at improving IRS by using the well-known distribution based method Bose-Einstein statistics (Bo1) as well as Linked Data from the knowledge base DBpedia using different numbers of expansion terms. We evaluated the effectiveness of each method individually as well as their combinations using two Text REtrieval Conference (TREC) test collections. Our approach has lead to significant improvement in terms of precision, recall, Mean Average Precision (MAP) at rank 10, and normalized Discounted Cumulative Gain (nDCG) at different ranks compared to Pseudo Relevance Feedback (PRF) that we used as a baseline. The results show that the inclusion of semantic annotations clearly improves the retrieval performance over the baseline method.

On the statistical distribution of the maxima of sine on random process

This study addresses the issue of statistics of maxima for a sine wave superimposed to a Gaussian noise, with particular focus on the maxima probability density function. Starting from the analysis of the well-known Rician Distribution, and of the hypotheses under which it was obtained, it is observed that this represents a valid solution only when the sine frequency is very close to that of random. However there are application of interest, especially in structural dynamics, where sine waves are, in the sense of frequency, before or after the random noise. For this reason the solution for the two cases mentioned above was calculated in terms of Probability Density Function, moving the very first step for application of spectral methods for structural analysis in case of Sine on Random excitation.

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution.

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.

Minimum Achievable Peak Age of Information Under Service Preemptions and Request Delay

There is a growing interest in analysing freshness of data in networked systems. Age of Information (AoI) has emerged as a relevant metric to quantify this freshness at a receiver, and minimizing this metric for different system models has received significant research attention. However, a fundamental question remains: what is the minimum achievable AoI in any single-server-single-source queuing system for a given service-time distribution? We address this question for the average peak AoI (PAoI) statistic by considering generate-at-will source model, service preemptions, and request delays. Our main result is on the characterization of the minimum achievable average PAoI, and we show that it is achieved by a fixed-threshold policy among the set of all causal policies. We use the characterization to provide necessary and sufficient condition for preemptions to be beneficial for a given service-time distribution. Our numerical results, obtained using well-known distributions, demonstrate that the heavier the tail of a distribution the higher the performance gains of using preemptions.

Marshall–Olkin Alpha Power Lomax Distribution: Estimation Methods, Applications on Physics and Economics

In this paper, we introduce and study a new extension of Lomax distribution with four-parameter named as the Marshall–Olkin alpha power Lomax (MOAPL) distribution. Some statistical properties of this distribution are discussed. Maximum likelihood estimation (MLE), maximum product spacing (MPS) and least Square (LS) method for the MOAPL distribution parameters are discussed. A numerical study using real data analysis and Monte-Carlo simulation are performed to compare between different methods of estimation. Superiority of the new model over some well-known distributions are illustrated by physics and economics real data sets. The MOAPL model can produce better fits than some well-known distributions as Marshall–Olkin Lomax, alpha power Lomax, Lomax distribution, Marshall–Olkin alpha power exponential, Kumaraswamy-generalized Lomax, exponentiated Lomax and power Lomax.

A Substorm Injection Event and the Radiation Belt Structure Observed by Space Radiation Detectors onboard Next Generation Small Satellite-1 (NEXTSat-1)

In this paper, we present observations of the Space Radiation Detectors (SRDs) onboard the Next Generation Small Satellite-1 (NEXTSat-1) satellite. The SRDs, which are a part of the Instruments for the study of Stable/Storm-time Space (ISSS), consist of the Medium-Energy Particle Detector (MEPD) and the High-Energy Particle Detector (HEPD). The MEPD can detect electrons, ions, and neutrals with energies ranging from 20 to 400 keV, and the HEPD can detect electrons over an energy range from 0.35 to 2 MeV. In this paper, we report an event where particle flux enhancements due to substorm injections are clearly identified in the MEPD A observations at energies of tens of keV. Additionally, we report a specific example observation of the electron distributions over a wide energy range in which we identify electron spatial distributions with energies of tens to hundreds of keV from the MEPD and with energy ranging up to a few MeV from the HEPD in the slot region and outer radiation belts. In addition, for an ~1.5-year period, we confirm that the HEPD successfully observed the well-known outer radiation belt electron flux distributions and their variations in time and L shell in a way consistent with the geomagnetic disturbance levels. Last, we find that the inner edge of the outer radiation belt is mostly coincident with the plasmapause locations in L, somewhat more consistent at subrelativistic energies than at relativistic energies. Based on these example events, we conclude that the SRD observations are of reliable quality, so they are useful for understanding the dynamics of the inner magnetosphere, including substorms and radiation belt variations.

State of Satiation Partially Regulates the Dynamics of Vertical Migration

Vertical migrations into shallower waters at night are beneficial for migrators as they reduce predation risk and allow migrators to encounter a higher density of prey. Nevertheless, ocean acoustics data and trawl data have shown that a portion of some vertically migrating populations remain at depth and do not migrate. One hypothesis for this phenomenon is the Hunger-Satiation hypothesis, which in part states that the non-migrating portion of the migrating species-assemblage refrains from migrating if they have full or partially full stomachs from daytime or nocturnal feeding. However, stomach fullness of the non-migrating subpopulation compared to the migrating portion has rarely been studied, due to the difficulty in obtaining sufficient samples. The stomach fullness levels of numerically abundant crustacean and fish species with well-known depth distributions were quantified in the present study. Animals were captured during night trawls from discrete-depth intervals between 0 and 1,500 m. Stomach fullness indices were assigned from 0 to 5 and compared between migratory taxa caught in shallow and deep waters. Data from the crustaceansAcanthephyra purpurea, Gardinerosergia splendens, Plesionika richardi, andSystellaspsis debilis, as well as the fishesLampanyctus alatus, Lepidophanes guentheri, andNotolychnus valdiviae, provided support for the Hunger-Satiation hypothesis, while data from the crustaceansGennadas capensisandGennadas valensand the fishBenthosema suborbitaledid not. These findings suggest that stomach vacancy may be just one of several factors regulating the dynamics of vertical migration in those species whose behavioral plasticity suggests daily “choices” in whether or not to vertically migrate.

Power Lomax Poisson Distribution: Properties and Estimation

A new four-parameter lifetime distribution named as the power Lomax Poisson is introduced and studied. The subject distribution is obtained by combining the power Lomax and Poisson distributions. Structural properties of the power Lomax Poisson model are implemented. Estimation of the model parameters are performed using the maximum likelihood, least squares and weighted least squares techniques. An intensive simulation study is performed for evaluating the performance of different estimators based on their relative biases, standard errors and mean square errors. Eventually, the superiority of the new compounding distribution over some existing distribution is illustrated by means of two real data sets. The results showed the fact that, the suggested model can produce better fits than some well-known distributions.

Generalized Asymmetric Laplace random fields: Existence and Application

Some specific random fields have been studied by many researchers whose finite-dimensional marginal distributions are multivariate closed skewnormal or multivariate extended skew-t, in time and spatial domains. In this paper, a necessary and sufficient condition is provided for applicability of such random field in spatial interpolation, based on the marginal distributions. Two deficiencies of the random fields generated by some well-known multivariate distributions are pointed out and in contrast, a suitable skew and heavy tailed random field is proposed. The efficiency of the proposed random field is illustrated through the interpolation of a real data.

Some Theoretical and Computational Aspects of the Inverse Generalized Power Weibull Distribution

This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.

Inference on a New Lifetime Distribution under Progressive Type II Censoring for a Parallel-Series Structure

A new lifetime distribution, called exponential doubly Poisson distribution, is proposed with decreasing, increasing, and upside-down bathtub-shaped hazard rates. One of the reasons for introducing the new distribution is that it can describe the failure time of a system connected in the form of a parallel-series structure. Some properties of the proposed distribution are addressed. Four methods of estimation for the involved parameters are considered based on progressively type II censored data. These methods are maximum likelihood, moments, least squares, and weighted least squares estimations. Through an extensive numerical simulation, the performance of the estimation methods is compared based on the average of mean squared errors and the average of absolute relative biases of the estimates. Two real datasets are used to compare the proposed distribution with some other well-known distributions. The comparison indicates that the proposed distribution is better than the other distributions to match the data provided.

A probabilistic-based analysis for wind distribution determination of a runway

PurposeThe purpose of this study is to describe precisely the wind speed regime and characteristics of a runway of an International Airport, the north-western part of Turkey.Design methodology approachThree different probability distributions, namely, Inverse Gaussian (IG), widely used two-parameter Weibull and Rayleigh distributions in the literature, are used to represent wind regime and characteristics of the runway. The parameters of each distribution are estimated by the pattern search (PS)-based heuristic algorithm. The results are compared with the other three methods-based numerical computation, including maximum-likelihood method, moment method (MoM) and power density method, respectively. To evaluate the fitting performance of the proposed method, several statistical goodness tests including the mostly used root mean square error (RMSE) and chi-squared (X2) are conducted.FindingsIn the light of the statistical goodness tests, the results of the IG-based PS attain better performance than the classical Weibull and Rayleigh functions. Both the RMSE and X2 values achieved by the IG-based PS method lower than that of Weibull and Rayleigh distributions. It exhibits a better fitting performance with 0.0074 for RMSE and 0.58 × 10−4 for X2 for probability density function (PDF) in 2012 and with RMSE of 0.0084 and X2 of 0.74 × 10−4 for PDF in 2013. As regard the cumulative density function of the measured wind data, the best results are found to be Weibull-based PS with RMSE of 0.0175 and X2 of 3.25 × 10−4 in 2012. However, Weibull-based MoM shows more excellent ability in 2013, with RMSE of 0.0166 and X2 of 2.94 × 10−4. Consequently, it is considered that the results of this study confirm that IG-based PS with the lowest error value can a good choice to model more accurately and characterize the wind speed profile of the airport.Practical implicationsThis paper presents a realistic point of view regarding the wind regime and characteristics of an airport. This study may cast the light on researchers, policymakers, policy analysts and airport designers intending to investigate the wind profile of a runway at the airport in the world and also provide a significant pathway on how to determine the wind distribution of the runway.Originality valueInstead of the well-known Weibull distribution for the representing of wind distribution in the literature, in this paper, IG distribution is used. Furthermore, the suitability of IG to represent the wind distribution is validated when compared with two-parameter Weibull and Rayleigh distributions. Besides, the performance and efficiency of PS have been evaluated by comparing it with other methods.

Decentralized Outages Prevention: A Remedial Action Scheme for Cyberattacks Targeting Market Retailers in Smart Distribution Systems

This article proposes a framework as a remedial action scheme (RAS) for close to real-time system operation when system operator becomes aware of possibility of decentralized outages due to simultaneous attacks on several market retailers. The upper level of the framework is an offline RAS where system operator immediately implements a customized reconfiguration preventing the decentralized outages. Due to immediate implementation of upper-level reaction, it is possible to face decentralized congestions in the new topology having minimum reliance on the attacked market retailers. Since severity of congestions is less than that of outages, the lower level of the framework is implemented as an online RAS. In this level, eligible nonattacked market retailers are invited into a secondary market to compete for generation/consumption redispatch and contribute into alleviation of congestions with the purpose of increasing their income. The effectiveness of the proposed framework is validated on a well-known 136-bus distribution system.