Showing papers on "K-distribution published in 2015"

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

Abstract: In this paper a comprehensive survey of the different methods of generating discrete probability distributions as analogues of continuous probability distributions is presented along with their applications in construction of new discrete distributions. The methods are classified based on different criterion of discretization.

On Families of Distributions with Shape Parameters

Abstract: Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi-dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on R with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all-important location and scale parameters. One important and useful family is comprised of the ‘skew-symmetric’ distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call ‘transformation of scale’—including two-piece distributions—and by probability integral transformation of non-uniform random variables. I also treat briefly the issues of multi-variate extension, of distributions on subsets of inline image and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal.

Novel formulation of the ℳ model through the Generalized-K distribution for atmospheric optical channels.

Abstract: In this paper, a novel and deeper physical interpretation on the recently published Malaga or ℳ statistical distribution is provided. This distribution, which is having a wide acceptance by the scientific community, models the optical irradiance scintillation induced by the atmospheric turbulence. Here, the analytical expressions previously published are modified in order to express them by a mixture of the known Generalized-K and discrete Binomial and Negative Binomial distributions. In particular, the probability density function (pdf) of the ℳ model is now obtained as a linear combination of these Generalized-K pdf, in which the coefficients depend directly on the parameters of the ℳ distribution. In this way, the Malaga model can be physically interpreted as a superposition of different optical sub-channels each of them described by the corresponding Generalized-K fading model and weighted by the ℳ dependent coefficients. The expressions here proposed are simpler than the equations of the original ℳ model and are validated by means of numerical simulations by generating ℳ -distributed random sequences and their associated histogram. This novel interpretation of the Malaga statistical distribution provides a valuable tool for analyzing the performance of atmospheric optical channels for every turbulence condition.

Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions

Abstract: We formalise and generalise the definition of the family of univariate double two–piece distributions, obtained by using a density–based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors.

A Two-Component $K$ –Lognormal Mixture Model and Its Parameter Estimation Method

Abstract: Statistical models are used for describing the synthetic aperture radar (SAR) image data and are the basis of SAR image interpretations. Appropriate statistical models that can accurately describe the SAR image data are essential for the performances of SAR image interpretations. A statistical model, which is a mixture of $K$ distribution and lognormal distribution, is proposed in this paper. This mixture model is able to model the clutter data, the target data, or the mixed data of clutter and target. This mixture model is also able to describe the proportions of clutter region and target region in a scene as well as the statistical properties of the clutter data and target data in the scene. A maximum likelihood method using the expectation–maximization approach is derived for estimating the parameters of the mixture model. Experiments have been conducted to demonstrate the effectiveness of the mixture model (together with the proposed parameter estimation method) for modeling the SAR data.

Flood frequency analysis using method of moments and L-moments of probability distributions

Abstract: Estimation of maximum flood discharge (MFD) at a desired location on a river is important for planning, design and management of hydraulic structures This can be achieved using deterministic models with extreme storm events or through frequency analysis by fitting of probability distributions to the recorded annual maximum discharge data In the latter approach, suitable probability distributions and associated parameter estimation methods are applied In the present study, method of moments and L-moments (LMO) are used for determination of parameters of six probability distributions Goodness-of-Fit tests such as Chi-square and Kolmogorov–Smirnov are applied for checking the adequacy of fitting of probability distributions to the recorded data Diagnostic test of D-index is used for the selection of a suitable distribution for estimation of MFD The study reveals that the Extreme Value Type-1 distribution (using LMO) is better suited amongst six distributions used in the estimation of MFD at Mal

Size-biased distributions in the generalized beta distribution family, with applications to forestry

Abstract: Size-biased distributions arise in many forestry applications, as well as other environmental, econometric, and biomedical sampling problems. We examine the size-biased versions of the generalized beta of the first kind, generalized beta of the second kind and generalized gamma distributions. These distributions include, as special cases, the Dagum (Burr Type III), Singh-Maddala (Burr Type XII) and Fisk distributions as well as better-studied distributions such as the Weibull, lognormal, beta (of the first and second kind), gamma and exponential. Our results indicate that specification and estimation of the size-biased forms of these distributions can be viewed within a unified framework. This should facilitate broader application of size-biased distributions in forestry sampling, modeling and analysis.

Stable Distributions as Noise Models for Molecular Communication

Abstract: In this work, we consider diffusion-based molecular communication timing channels. Three different timing channels are presented based on three different modulation techniques, i.e., i) modulation of the release timing of the information particles, ii) modulation on the time between two consecutive information particles of the same type, and iii) modulation on the time between two consecutive information particles of different types. We show that each channel can be represented as an additive noise channel, where the noise follows one of the subclasses of stable distributions. We provide expressions for the probability density function of the noise terms, and numerical evaluations for the probability density function and cumulative density function. We also show that the tails are longer than Gaussian distribution, as expected.

On the Harris extended family of distributions

Abstract: A new method for generating new classes of distributions based on the probability-generating function is presented in Aly and Benkherouf [A new family of distributions based on probability generating functions. Sankhya B. 2011;73:70–80]. In particular, they focused their interest to the so-called Harris extended family of distributions. In this paper, we provide several general results regarding the Harris extended models such as the general behaviour of the failure rate function. We also derive a very useful representation for the Harris extended density function as an absolutely convergent power series of the survival function of the baseline distribution. Additionally, some stochastic order relations are established and limiting distributions of sample extremes are also considered for this model. These general results are illustrated in several special Harris extended models. Finally, we discuss estimation of the model parameters by the method of maximum likelihood and provide an application to real da...

Using fractal dimension to target detection in bistatic SAR data

Abstract: This paper proposes an algorithm for estimating the fractal dimension of real sea bistatic synthetic aperture radar data. The algorithm is based on the use of the fractal dimension estimated by the box counting method to detect the sub-data which contain the targets. Based on this approach, the performance of the fractal detector proposed in this paper was demonstrated by the evaluation of the probability of detection by means of Monte Carlo simulation and was verified that we can use the fractal dimension to distinguish between targets and clutter, even for a small signal-to-noise ratio.

Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions

Abstract: One of the problems that appear in reliability and survival analysis is how we choose the best distribution that fitted the data. Sometimes we see that the handle data have two fitted distributions. Both inverse Gaussian and gamma distributions have been used among many well-known failure time distributions with positively skewed data. The problem of selecting between them is considered. We used the logarithm of maximum likelihood ratio as a test for discriminating between these two distributions. The test has been carried out on six different data sets.

SAR probability density function estimation using a generalized form of K-distribution

Abstract: In this paper, generalized forms of amplitude and intensity K-distributions are proposed to model multilook synthetic aperture radar (SAR) data. The approach is based upon a product model in which the amplitude and intensity distributions of the SAR backscatter component are assumed to be Laguerre orthogonal expansions of the traditional clutter distribution. The SAR intensity and amplitude probability density functions (pdfs) are derived and turn out to be the weighted combination of a series of K-distributions. Several theoretical and implementation issues regarding the proposed generalization are discussed. Comparative experimental results using real SAR data indicates that these generalized forms of K may allow better estimation of the SAR pdf than that of the traditional K distribution.

Distributions of Runs Revisited

Abstract: Distributions of runs have important applications in many fields, including biological sequence analysis. The generating function (GF) method provides a unified approach to tackle different run-related problems in multistate trials. By utilizing this method, various run-related distributions are derived in a systematic way for both conditional and unconditional models. The GF approach also naturally yields the asymptotic distributions. For all the distributions considered, the limiting distributions are Gaussian, with mean, variance, and covariance linear functions in the size of the system.

The complementary Poisson-Lindley class of distributions

Abstract: This paper proposed a new general class of continuous lifetime distributions, which is a complementary to the Poisson-Lindley family proposed by Asgharzadeh et al. [3]. The new class is derived by compounding the maximum of a random number of independent and identically continuous distributed random variables, and Poisson-Lindley distribution. Several properties of the proposed class are discussed, including a formal proof of probability density, cumulative distribution, and reliability and hazard rate functions. The unknown parameters are estimated by the maximum likelihood method and the Fisher’s information matrix elements are determined. Some sub-models of this class are investigated and studied in some details. Finally, a real data set is analyzed to illustrate the performance of new distributions.

A new distribution function with bounded support: the reflected Generalized Topp-Leone Power Series distribution

Abstract: In this paper we introduce a new flexible class of distributions with bounded support, called reflected Generalized Topp-Leone Power Series (rGTL-PS), obtained by compounding the reflected Generalized Topp-Leone (van Drop and Kotz, 2006) and the family of Power Series distributions. The proposed class includes, as special cases, some new distributions with limited support such as the rGTL-Logarithmic, the rGTL-Geometric, the rGTL-Poisson and rGTL-Binomial. This work is an attempt to partially fill a gap regarding the presence, in the literature, of continuous distributions with bounded support, which instead appear to be very useful in many real contexts, included the reliability. Some properties of the class, including moments, hazard rate and quantile are investigated. Moreover, the maximum likelihood estimators of the parameters are examined and the observed Fisher information matrix provided. Finally, in order to show the usefulness of the new class, some applications to real data are reported.

System and method for interferometrically tracking objects using a low-antenna-count antenna array

Abstract: A radio-frequency interferometry method for determining parameters of motion of a moving object from phase difference information from an antenna baseline formed of two antennas. At each of a plurality of observation events, compute a posterior probability density function from the phase differences from the baseline, separate the modes with a threshold value of probability density, and compute a probability of each mode. For each possible sequence of modes, determine a mode sequence probability as the product of the probabilities of each mode in that sequence, estimate a χ 2 goodness of fit function based on an assumed type of motion. Determine the net probability of each possible sequence of modes as the product of a relative probability derived from the χ 2 and the mode sequence probability. Alternately, two or more parallel or colinear baselines are used, and the posterior PDF is a combined PDF over each of the baselines.

Method for Generating Distributions and Classes of Probability Distributions: The Univariate Case

Abstract: In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction In this method, distribution classes are built from pre-defined monotonic functions and from known distributions With the use of this method, we can obtain different classes of probability distributions described in literature Beside these results, we could obtain results on the support and nature of the generated distributions

Reliability analysis of load-sharing m-out-of-n systems with arbitrary load and different probability distributions of time to failure

Abstract: The reliability analysis of load-sharing m-out-of-n systems where the workload is shared by the remaining working units when a unit fails is proposed in the paper. General expressions are provided for the m-out-of-n system reliability by arbitrary probability distributions of time to failure of units. Simplified methods are given for computing the survivor function in cases when the time to unit failure is governed by the Weibull and exponential probability distributions. The system survivor function and the mean time to failure in the explicit form are obtained for systems with arbitrary load (decreasing and increasing) by the exponential time to unit failure. Numerical examples illustrate the properties of load-sharing m-out-of-n systems.

Characterizations of continuous probability distributions occurring in physics and allied sciences by truncated moment

Abstract: A probability distribution can be characterized through various methods. Before a particular probability distribution model is applied to fit the real-world data, it is necessary to confirm whether the given continuous probability distribution satisfies the underlying requirements by its characterization. In this paper, characterizations of some continuous probability distributions occurring in physics and allied sciences have been established. We have considered the normal, Laplace, Lorentz, logistic, Boltzmann, Rayleigh, log-normal, Maxwell, Fermi-Dirac, and Bose-Einstein distributions, and characterized them by applying a truncated moment method; that is, by taking a product of reverse hazard rate and another function of the truncated point. It is hoped that the proposed characterizations will be useful for researchers in various fields of physics and allied sciences.

Application of the fractional-stable distributions for approximation of the gene expression profiles.

Abstract: Nowadays, there are reliable scientific data highlighting that the probability density function of the gene expression demonstrates a number of universal features commonly observed in the microarray experiments. First of all, these distributions demonstrate the power-law asymptotics and, secondly, the shape of these distributions is inherent for all organisms and tissues. This fact leads to appearance of a number of works where authors investigate various probability distributions for an approximation of the empirical distributions of the gene expression. Nevertheless, all these distributions are not a limit distribution and are not a solution of any equation. These facts, in our opinion, are essential shortcoming of these probability laws. Besides, the expression of the individual gene is not an accidental phenomenon and it depends on the expression of the other genes. This suggests an existence of the genic regulatory net in a cell. The present work describes the class of the fractional-stable distributions. This class of the distributions is a limit distribution of the sums of independent identically distributed random variables. Due to the power-law asymptotics, these distributions are applicable for the approximation of the experimental densities of the gene expression for microarray experiments. The parameters of the fractional stable distributions are statistically estimated by experimental data and the functions of the empirical and theoretical densities are compared. Here we describe algorithms for simulation of the fractional-stable variables and estimation of the parameters of the the fractional stable densities. The results of such a comparison allow to conclude that the empirical densities of the gene expression can be approximated by the fractional-stable distributions.

K Distribution Sea Clutter Modeling and Simulation Based on ZMNL

Abstract: This paper introduces the method of constructing the sea clutter, sea clutter amplitude distribution and power spectrum distribution characteristics of the model, using the ZMNL method of the K distribution sea clutter simulation, simulation results show that, it greatly reduces the amount of computation based on ZMNL method of K Distribution Sea Clutter Modeling and Simulation, improves the simulation speed.

Simulation method and system of radar sea clusters

Abstract: The invention discloses a simulation method and system of radar sea clusters. The method comprises: generating a random sequence of a composite K distribution model; generating a random sequence with a space correlation characteristic out of the generated random sequence through a space correlation filter; and performing Kai distribution power modulation on the random sequence with the space correlation characteristic to obtain a sea cluster space image. By using the simulation method and system provided by the invention, the multiple texture characteristics and statistics characteristic of the sea clusters can be accurately described, and the simulation degree of sea cluster simulation is improved.

Frequency Analysis of Annual Maximum Flood Discharge Using Method of Moments and Maximum Likelihood Method of Gamma and Extreme Value Family of Probability Distributions

Abstract: Estimation of Maximum Flood Discharge (MFD) for a given return period is important for planning, design and management of hydraulic structures for the project. This can be achieved through Flood Frequency Analysis (FFA) by fitting of probability distributions to the recorded Annual Maximum Discharge (AMD) data. In this paper, Gamma and Extreme Value family of probability distributions are adopted in FFA. Method of Moments and Maximum Likelihood Method are used for determination of parameters of six probability distributions. Goodness-of-Fit tests such as Chi-square and KolmogorovSmirnov are applied for checking the adequacy of fitting of probability distributions to the recorded AMD data. Diagnostic test of D-index is used for the selection of a suitable distribution for estimation of MFD. The study showed that the exponential distribution (using MLM) is found to be better suited amongst six distributions adopted in estimation of MFD at Dedtalai and gamma distribution (using MLM) for Ghala.

Some Properties of Gamma Generated Distributions

Abstract: Based on standard probability distributions, new families of univariate distributions have been introduced and their properties studied by many authors. The present paper investigates some general properties of a family of Gamma generated distributions proposed by Zografos and Balakrishnan (2009).

Stochastic orders in the Bayesian framework

Abstract: We give a review and a cross section of stochastic ordering problems from the Bayesian point of view – the stochastic ordering of posterior distributions, marginal distributions of data and predictive distributions under order assumptions on sampling distributions and prior distributions. The importance for risk theory and application to actuarial problems are commented.