Well-known Distribution Research Articles

On the posterior property of the Rician distribution

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles – Sustainable, Accurate, Fair, and Explainable – ensuring robustness, fairness, and transparency in predictive modelling.

Reliability Analysis for Unknown Age Class of Lifetime Distribution with Real Applications in Medical Science

Analyzing the reliability of the aging class of life distribution provides important information about how long a product lasts and sustainability measures that are essential for determining the environmental impact and formulating resource-saving plans. The study emphasizes the goodness-of-fit technique of the nonparametric test for the NBRUmgf class because age data are crucial for applications. Evaluations were conducted using the test’s asymptotic properties and Pitman efficiency methodology for some selected asymmetric probability models, and the outcomes were compared with those of alternative methods. We assessed the test’s power against widely used reliability distributions for some well-known alternative asymmetric distributions, including the Weibull, Gamma, and linear failure rate (LFR) distributions, and provided percentiles for both censored and uncensored data. This study shows the efficacy of the test in various sectors using real-world datasets and comprehensive tables of test statistics.

Size-polydispersity-induced effects on the structure of active Brownian pseudo-hard disks

Studies of the effects of particle-size polydispersity or of particle interactions on active matter have been limited to determine and analyze the system short-time dynamics in the high-density regime. On the other hand, the effects of polydispersity on the structural behavior of active systems are of relevance and have received much less attention. In this paper, we comprehensively analyze the effects of size dispersion of pseudo hard-disk active Brownian particles, on its structural behavior at different system densities and different self-propelling velocities, thus elucidating the interplay of these features with the polydispersity. This is introduced into our analysis by well-known particle size distributions in such a manner that the average size is fixed, but with a variance that accounts for different dispersion of the particle size according to: Gaussian, Weibull, uniform and “two point” distribution. Local and global structural properties of the system are determined under these considerations. We observe that activity and size polydisperse effects become relevantly conspicuous at densities above the motility induced phase separation critical point of the monodispersal fluid. We notice that, while the activity promotes a more defined local and global structural arrangement, the polydispersity decreases such structure, observing the greatest effect when the particle size is defined by a uniform distribution.

Recovering chemical bimodalities in observed edge-on stellar disks: Insights from AURIGA simulations

The well-known bimodal distribution of Milky Way disk stars in the [α/Fe]–metallicity plane is often used to define thick and thin disks. In external edge-on galaxies, there have been attempts to identify this type of bimodality using integral field spectroscopy (IFS) data. However, for unresolved stellar populations, observations only contain integrated information, making these studies challenging. We assessed the ability to recover chemical bimodalities in IFS observations of edge-on galaxies, using 24 Milky Way-mass galaxies from the AURIGA zoom-in cosmological simulations. We first analyzed the distribution of single stellar particles in the [Mg/Fe]–[Fe/H] plane, finding that bimodality is frequent but not ubiquitous and often unclear. Then we produced mock IFS [Mg/Fe] and [Fe/H] maps of galaxies seen edge on, and considered integrated stellar-population properties (projected and spatially binned). We investigated how the distribution of stars in the [Mg/Fe]–[Fe/H] plane is affected by edge-on projection and spatial binning. Bimodality is preserved, while distributions change their shapes. Naturally, broad distributions of individual star particles are narrowed into smaller [Mg/Fe] and [Fe/H] ranges for spatial bins. We observe continuous distributions from high [Mg/Fe] and low [Fe/H], to lower [Mg/Fe] values and higher [Fe/H]. Despite being continuous, these distributions are bimodal in most cases. The overlap in [Fe/H] is small, and different [Mg/Fe] components show up as peaks instead of sequences (even when the latter are present for individual particles). The larger the spatial bins, the narrower the [Mg/Fe]–[Fe/H] distribution. This narrowing helps amplify the density of different [Mg/Fe] peaks, often leading to a clearer bimodality in mock IFS observations than for original star particles. We also assessed the correspondence of chemical bimodalities with the distinction between geometric thick and thin disks. Their individual particles have different distributions, but mostly overlap in [Mg/Fe] and [Fe/H]. However, integrated properties of geometric thick and thin disks in mock maps do mostly segregate into different regions of the [Mg/Fe]–[Fe/H] plane. In bimodal distributions, they correspond to the two distinct peaks. Our results show that this approach can be used for bimodality studies in future IFS observations of edge-on external galaxies.

A new class of Lindley distribution: System reliability, simulation and applications

This paper presents a new probability distribution called the DUS Lindley distribution, created by applying the DUS transformation to the traditional Lindley distribution. The study provides an in-depth analysis of the distribution's statistical properties. These properties include a variety of statistical measures such as the probability density function, cumulative distribution function, failure rate, survival function, reverse hazard function, Mills ratio, mean residual life, mean past life, moments, conditional moments, characteristic function, order statistics, entropy measures, likelihood ratio test and Lorenz and Bonferroni curves. Parameter estimation is performed using several methods including weighted least squares, maximum likelihood estimation, Cramer-Von Mises estimation, least squares and Anderson-Darling estimation. The paper also explores the estimation of system reliability and evaluates the performance of maximum likelihood estimators through simulation studies across different sample sizes. Finally, the DUS Lindley distribution is applied to two real-world datasets, demonstrating a better fit than other well-known distributions.

Fluctuations and Power Low Distribution Function in Nonequilibrium Systems

The Fokker–Planck equation is formulated for the distribution functions of macroscopic open systems in the space of slowly changing physical variables (energy, adiabatic invariants, etc.). The stationary solution of such equations determines a quasi-equilibrium distribution function in the relevant space. The proposed approach involves the evolution of systems under the action of dissipation and diffusion in the space of the appropriate variables. It is shown that the well-known power law distribution can be obtained by considering internal and external fluctuations in statistical systems.

Mean Absolute Deviation (About Mean) Metric for Kurtosis

In this paper, we introduce a MAD (about mean) alternative metric to classical kurtosis. Using the formula for mean absolute deviation, we identify two special points and construct the corresponding distributions with these reference points as their means. The proposed alternative is computed from mean absolute deviations for these distributions. These measures are bounded, require only the existence of first-order moments, and are easy to interpret. We illustrate the computation of these measures for several well-known distributions.

Quantitative and Qualitative Analysis of Aircraft Round-Trip Times Using Phase Type Distributions

One of the major issues facing commercial airlines is the time that it takes to board passengers. Further, most airlines wish to increase the number of trips that an aircraft can make between two or more cities. Thus, reducing the overall boarding times by a few minutes will have a significant impact on the number of trips made by an aircraft, as well as enabling improvements in key measures such as the median and 75th and 95th percentiles. Looking at such measures other than the mean is critical as it is well known that the mean can under- or overestimate the performance of any model. While there is considerable literature on the study of strategies to decrease boarding times, the same cannot be said about the study of the boarding time given a particular strategy for boarding. Thus, the focus of this paper is to study analytically (using suitable stochastic models) and numerically the impact of reducing the average time on the key measures to help the system to plan accordingly. This is achieved using a well-known probability distribution, namely the phase type distribution, to model various events involved in the boarding process. Illustrative numerical results show a reduction in the percentile values when the average boarding times are decreased. Understanding the percentiles of the boarding times, as opposed to relying only on the average boarding times, will help management to adopt a better boarding strategy that in turn will lead to an increase in the number of trips that an aircraft can make.

Ultraviolet laser-induced fragmentation of hydrocarbon fuel droplets

The present study aims to understand droplet fragmentation due to instabilities from the radiative heating process. We focus on the plasma-induced breakup mechanism of iso-octane and n-hexane droplets from the nucleation of holes through sheets and instabilities. The plasma generation inside the droplets leads to an intense explosion followed by fragmentation of the droplets. A droplet is suspended in the air using an acoustic levitator and exposed to ultraviolet nanosecond laser pulses. The droplet sizes used are in the range of 0.5–2 mm in diameter, and laser energies are 10–20 mJ per pulse. Initially, plasma formation followed by shock wave emission is observed during the impact of the laser pulse. Afterward, the droplet opens at one side and is stretched vertically to form a liquid sheet. The hole formation and its rapid growth result in the breaking of the thin liquid sheet. Small droplets and ligaments emerge from the circular edge of the sheet, which follows the well-known ligament distribution. This study reveals the detailed analysis of expansion dynamics, evolution of single and multiple holes, and instabilities associated with the liquid sheet. The results observed are categorized into four different mechanisms: (1) plasma formation followed by shock wave propagation, (2) droplet deformation, (3) sheet breakup through nucleation of holes followed by rapid growth, and (4) complete atomization.

Nakagami Distribution for Modeling Monthly Precipitations in Van, Türkiye

Precipitation patterns are intricately influenced by geographic factors and local environmental conditions. Statistical distributions are one of the methods that help investigate precipitation characteristics at different sites. Van is a province that ranks among the provinces with the lowest precipitation in the Eastern Anatolia region of Türkiye, receiving an annual rainfall of around 400 mm. In this study, 63 years of monthly average precipitation data from Van, are modeled employing various well-known statistical distributions including the Nakagami distribution. The Nakagami distribution is one of the flexible distributions used in describing data from various fields. In estimating the parameters of the considered distributions maximum likelihood estimation method is utilized. Comparisons are made using various goodness of fit criteria including root mean squared error, coefficient of determination, and Kolmogorov-Smirnov test. According to the results, the Nakagami distribution is found to be the most suitable statistical distribution for modeling precipitations in Van province. Additionally, precipitation values for 10, 25, 50, and 100-year return periods are obtained.

Rise and Fall of Light Top Squarks in the LHC Top-Quark Sample.

We discuss the possibility that light new physics in the top-quark sample at the LHC can be found by investigating with greater care well-known kinematic distributions, such as the invariant mass m_{bℓ} of the b-jet and the charged lepton in fully leptonic tt[over ¯] events. We demonstrate that new physics can be probed in the rising part of the already measured m_{bℓ} distribution. To this end, we analyze a concrete supersymmetric scenario with a light right-handed top-squark, chargino and neutralino. The corresponding spectra are characterized by small mass differences, which make them not yet excluded by current LHC searches and give rise to a specific end point in the shape of the m_{bℓ} distribution. We argue that this sharp feature is general for models of light new physics that have so far escaped the LHC searches and can offer a precious handle for the implementation of robust searches that exploit, rather than suffer from, soft bottom quarks and leptons. Recasting public data on searches for new physics, we identify candidate models that are not yet excluded. For these models, we study the m_{bℓ} distribution and derive the expected signal yields, finding that there is untapped potential for discovery of new physics using the m_{bℓ} distribution.

A novel skewed generalized normal distribution: properties, statistical inference, and its applications

In this paper, a novel skewed generalized normal distribution (NSGN), which encompasses several well-known distributions, is a two-component mixture model based on the generalized normal distribution. The NSGN distribution offers flexibility in modeling skewed data characterized by high kurtosis and strong skewness, making it highly applicable in finance, medicine, and engineering. The primary characteristics and properties of this new distribution are introduced, and the explicit expressions for the moments of order statistics are provided using recursive relations. The maximum likelihood estimation based on a profile likelihood approach, L-moments estimation, and a two-step estimation method combining Bayesian posterior maximum estimation with moment estimates are presented to estimate the four parameters of NSGN distribution. A simulation study compares the performance of these methods across different sample sizes and different parameters. The appropriateness of the proposed distribution has been tested by comparing it with several skewed distributions. Additionally, applications to real datasets showcase the beneficial properties of the NSGN for applied statistical research.

Random uptake of nanoparticles by cells and negative binomial distributions of pits

AbstractThis paper focuses on a key experimental observation concerning the random internalization of nanoparticles by cells: the occurrence of over-dispersion in nanoparticle uptake which can be characterized by a negative binomial distribution. We compare the well-known distribution with the empirical distribution of pits on the surface of an alveolar macrophage. We find that a negative binomial distribution provides the accurate curve-fit model for the observed pit distribution.

Properties, quantile regression, and application of bounded exponentiated Weibull distribution to COVID-19 data of mortality and survival rates

Well-known continuous distributions such as Beta and Kumaraswamy distribution are useful for modeling the datasets which are based on unit interval [0,1]. But every distribution is not always useful for all types of data sets, rather it depends on the shapes of data as well. In this research, a three-parameter new distribution named bounded exponentiated Weibull (BEW) distribution is defined to model the data set with the support of unit interval [0,1]. Some fundamental distributional properties for the BEW distribution have been investigated. For modeling dependence between measures in a dataset, a bivariate extension of the BEW distribution is developed, and graphical shapes for the bivariate BEW distribution have been shown. Several estimation methods have been discussed to estimate the parameters of the BEW distribution and to check the performance of the estimator, a Monte Carlo simulation study has been done. Afterward, the applications of the BEW distribution are illustrated using COVID-19 data sets. The proposed distribution shows a better fit than many well-known distributions. Lastly, a quantile regression model from bounded exponentiated Weibull distribution is developed, and its graphical shapes for the probability density function (PDF) and hazard function have been shown.

Evaluating the uncertainty in mean residual times: Estimators based on residence times from discrete time processes

In this work, we propose estimators for the variance of mean residual times, which rely on individual residence times. The latter are assumed to be described by independent and identically distributed random variables, generated by a discrete-time stochastic process. We examine their performance through numerical experiments involving well-known probability distributions, and an application example using molecular dynamics simulation results, from an aqueous NaCl solution, is provided. These computationally inexpensive estimators, capable of achieving very accurate outcomes, serve as useful tools for assessing and reporting uncertainties in mean residual times across a wide range of simulations.

A STOCHASTIC MODEL FOR LENGTH BIASED LOAI DISTRIBUTION WITH PROPERTIES AND ITS APPLICATIONS

One of the most important applications of statistical analysis is in health research and application. Cancer studies are mostly required special statistical considerations in order to find the appropriate model for fitting the survival data. In this paper, we examine some general models leading to a weighted distribution. The developed distribution, also known as the length biased model, is referred to as the length biased Loai distribution. This distribution is a specific type of basic distribution, the Loai distribution. The length biased distribution has been compared with the original distribution. Some statistical properties of this distribution are derived, such as moments, the moment generating function, the reliability analysis, and the included functions. Also, the distribution of order statistics, quantile function, and likelihood ratio test are presented. The Bonferroni and Lorenz carvers, as well as the Rnyi and Tsallis entropies, are derived. The method of maximum likelihood estimation is used to estimate the distribution parameters. A simulation study is performed to investigate the performance of the estimation. The real data applications demonstrate that the proposed distribution can provide better results than several well-known distributions.

Characterizations of continuous log-symmetric distributions based on properties of order statistics

The class of log-symmetric distributions is a generalization of log-normal distribution and includes some well-known distributions such as log-normal, log-logistic, log-Laplace, log-Cauchy, log-power-exponential, log-student-t, log-slash, and Birnbaum-Saunders distributions. In this paper, several characterization results are obtained for log-symmetric distributions based on moments of some functions of the parent distribution and also on the basis of some properties of order statistics. Specifically, when X is identical in distribution with a decreasing continuous function h ( X ) , then a relationship is established between upper and lower order statistics which is then utilized to construct characterization results for log-symmetric distributions in terms of functions of order statistics. The established results can be used for constructing a goodness-of-fit test for log-symmetric distributions.

Genomic signatures of hybridization between Ixodes ricinus and Ixodes persulcatus in natural populations.

Identifying hybridization between common pathogen vectors is essential due to the major public health implications through risks associated with hybrid's enhanced pathogen transmission potential. The hard-ticks Ixodes ricinus and Ixodes persulcatus are the two most common vectors of tick-borne pathogens that affect human and animal health in Europe. Ixodes ricinus is a known native species in Finland with a well-known distribution, whereas I. persulcatus has expanded in range and abundance over the past 60 years, and currently it appears the most common tick species in certain areas in Finland. Here we used double-digest restriction site-associated DNA (ddRAD) sequencing on 186 ticks (morphologically identified as 92 I. ricinus, and 94 I. persulcatus) collected across Finland to investigate whether RAD generated single nucleotide polymorphisms (SNPs) can discriminate tick species and identify potential hybridization events. Two different clustering methods were used to assign specific species based on how they clustered and identified hybrids among them. We were able to discriminate between the two tick species and identified 11 putative hybrids with admixed genomic proportions ranging from approximately 24 to 76 percent. Four of these hybrids were morphologically identified as I. ricinus while the remaining seven were identified as I. persulcatus. Our results thus indicate that RAD SNPs are robust in identifying both species of the ticks as well as putative hybrids. These results further suggest ongoing hybridization between I. ricinus and I. persulcatus in their natural populations in Finland. The unique ability of RAD markers to discriminate between tick species and hybrids adds a useful aspect to tick evolutionary studies. Our findings align with previous studies and suggest a shared evolutionary history between the species, with instances of individuals possessing a considerable proportion of the other species' genome. This study is a significant step in understanding the formation of hybridization zones due to range expansion potentially associated with climate change.

Seismic data filtering using deconvolutive short-time Fourier transform

Cohen class distributions are well-known time-frequency distributions that have been widely used to analyze different signals. However, they are impractical for signal filtering because they only provide amplitude spectra and suffer from cross terms. In this paper, deconvolutive short-time Fourier transform (DSTFT) is developed by estimating phase spectra and updating moduli to address residual cross terms. The DSTFT moduli is used as weights and apply a weighted least-squares technique to estimate a high-resolution and almost cross-term-free Wigner-Ville distribution. Through numerical tests, it has been found that choosing the optimal window length can minimize cross terms in short-time Fourier transform and DSTFT spectrograms. Furthermore, using thresholding or reweighting techniques can effectively eliminate weights associated with noise. The performance of our method is demonstrated using synthetic and two real seismic wavefield separation problems, including ground-roll removal in seismic shot records and polarization analysis in seismology. The results indicate the high performance of our method in estimating phase spectra and filtering seismic data.

Medical application with an extended Ailamujia inverted Weibull model: Properties, estimation and simulation

In this article, we propose a new lifetime model called Kavya-Manoharan Ailanujia inverted Weibull distribution, which is obtained from the Kavya-Manoharan (KM) transformation family and Ailanujia inverted Weibull distribution. Various statistical properties are obtained, involving moments, incomplete moments, conditional moments, mean deviations, mean residual lifetime and mean past lifetime and entropy. Moreover, the newly proposed distribution, characterized by two parameters, proves to be remarkably versatile, as demonstrated in the application results. Several statistical properties of the KMAIW distribution are deduced, and the estimation of its parameters is accomplished through three distinct techniques. To assess the effectiveness of these approaches, a comprehensive simulation study is conducted. The significance and applicability of the proposed model are underscored through the analysis of a real-world dataset. In comparative evaluations against well-known distributions featuring two, three, and four parameters, the suggested model consistently outperforms them all. This highlights the superior fitting capability and adaptability of the proposed model in comparison to established distributions with varying parameter complexities.