Truncated Probability Distribution Research Articles

Modeling dispersal using capture–recapture data: A comparison of dispersal models

AbstractCapture–recapture methods have been a cornerstone of field‐based dispersal ecology. However, obtaining unbiased estimates of dispersal parameters from capture–recapture data is challenging because it is impossible to survey all possible range of dispersal in the field. There are several approaches to address this critical issue of capture–recapture methods. Still, a lack of formal comparisons among these modeling approaches has confused about which is the best practice given the available dataset. Here, I compared the performance of three dispersal models using test datasets simulated under various sampling designs. In the first approach, a probability distribution (a dispersal kernel) was simply fitted to the capture–recapture data (the “simple dispersal model”). In the second approach, a truncated probability distribution was used to account for the finite range of observations (the “truncated dispersal model”). Finally, the dispersal and observation processes were coupled to consider the spatial organization of sampling designs (the “dispersal–observation model”). The simulation study provided three important insights. First, the dispersal–observation model provided reliable estimates of dispersal parameters, even under sampling designs with a few recaptures. Second, the truncated dispersal model was also effective, but only when the number of recaptures was large. Finally, the use of the simple dispersal model caused a substantial underestimation of dispersal parameters regardless of sampling designs; this modeling approach should be avoided where possible. The results of this simulation study should help choose a suitable modeling approach.

Speech emotion recognition using discriminative dimension reduction by employing a modified quantum-behaved particle swarm optimization algorithm

In recent years, Speech Emotion Recognition (SER) has received considerable attention in affective computing field. In this paper, an improved system for SER is proposed. In the feature extraction step, a hybrid high-dimensional rich feature vector is extracted from both speech signal and glottal-waveform signal using techniques such as MFCC, PLPC, and MVDR. The prosodic features derived from fundamental frequency (f0) contour are also added to this feature vector. The proposed system is based on a holistic approach that employs a modified quantum-behaved particle swarm optimization (QPSO) algorithm (called pQPSO) to estimate both the optimal projection matrix for feature-vector dimension reduction and Gaussian Mixture Model (GMM) classifier parameters. Since the problem parameters are in a limited range and the standard QPSO algorithm performs a search in an infinite range, in this paper, the QPSO is modified in such a way that it uses a truncated probability distribution and makes the search more efficient. The system works in real-time and is evaluated on three standard emotional speech databases Berlin database of emotional speech (EMO-DB), Surrey Audio-Visual Expressed Emotion (SAVEE) and Interactive Emotional Dyadic Motion Capture (IEMOCAP). The proposed method improves the accuracy of the SER system compared to classical methods such as FA, PCA, PPCA, LDA, standard QPSO, wQPSO, and deep neural network, and also outperforms many state-of-the-art recent approaches that use the same datasets.

Modeling the Interior of Black Holes Utilizing a 4-D Spatial Blackbody Radiation Model with an Exponential Distribution

This is a second follow up paper on a model, which treats the black hole as a 4-D spatial ball filled with blackbody radiation. For the interior radiative mass distribution, we employ a new type of truncated probability distribution function, the exponential distribution. We find that this distribution comes closest to reproducing a singularity at the center, and yet it is finite at 4-D radius, . This distribution will give a constant gravitational acceleration for a test particle throughout the black hole, irrespective of radius. The 4-D gravitational acceleration is given by the expression, , where R is the radius of the black hole, MR is its mass, and is the exponential shape parameter, which depends only on the mass, or radius, of the black hole. We calculate the gravitational force, and the entropy within the black hole interior, as well as on its surface, identified as the event horizon, which separates 3-D from 4-D space. Similar to a truncated Gaussian distribution, the gravitational force increases discontinuously, and dramatically, upon entry into the 4-D black hole from the 3-D side. It is also radius dependent within the 4-D black hole. Moreover, the total entropy is shown to be much less than the Bekenstein result, similar to the truncated Gaussian. For the gravitational force, we obtain, , where Mr is the radiative mass enclosed within a 4-D volume of radius r. This unusual force law indicates that the gravitational force acting upon a layer of blackbody photons at radius r is strictly proportional to the enclosed radiative energy, MrC2, contained within that radius, with 0.1λ being the constant of proportionality. For the entropy at radius, r, and on the surface, we obtain an expression which is order of magnitude comparable to the truncated Normal distribution. Tables are presented for three black holes, one having a mass equal to that of the sun. The other two have masses, which are ten times that of the sun, and 106 solar masses. The corresponding parameters are found to equal, , respectively. We compare these results to the truncated Gaussian distribution, which were worked out in another paper.

Modeling of truncated probability distributions

A method for modeling truncated probability distributions based on the transformation of some basic distribution is developed. One of the parameters of the simulated distributions is a quantile of arbitrary order. The cases of the initial multiplication of the basic density function by linear and quadratic factors are considered. In the case of the basic normal law with linear multipliers, expressions for the density and the first moments are generally presented. Using different base distributions and varying parameters leads to a wide class of new distributions. The results of the work can be useful in the processing of statistics with a non-standard structure.

Truncation thresholds: a pair of spike detection thresholds computed using truncated probability distributions

Truncation thresholds: a pair of spike detection thresholds computed using truncated probability distributions

Structure buckling hybrid reliability analysis of a supercavitating projectile using a model with truncated probability and multi-ellipsoid convex set uncertainties

ABSTRACTStructure buckling problems for supercavitating projectiles are often observed in high underwater velocity operating conditions. As a result, it is necessary to perform a structure buckling reliability analysis. It is common that \\hboxprobabilistic and nonprobabilistic uncertainty information exist simultaneously. Also, it is reasonable that probability distributions of most random variables in engineering are treated as truncated probability distributions. In this paper, a new hybrid model is proposed, which deals with structure performance function with both truncated probability distribution variables and multi-ellipsoid convex set variables. The model discussed here is adapted for two separate cases in the standard super-sphere space, i.e., limit state surface interferences with a unit super-sphere region or not. The hybrid reliability index is calculated using a modified limit step length iteration algorithm to ensure convergence. Good convergence and validity of the iteration algorithm are verified using numerical examples with highly nonlinear structure performance function. The hybrid model is applied to the structure buckling hybrid reliability analysis of a supercavitating projectile. Results show that structure buckling hybrid reliability index increases with the increase in the ratio of base diameter to cavitator diameter, and decreases with the increase of initial launch velocity. Also, uncertainty degree of cavitator drag coefficient and initial launch velocity should be controlled in demonstration for high structure buckling reliability of supercavitating projectiles.

A Weibull Approach for Improving Climate Model Projections of Tropical Cyclone Wind-Speed Distributions

AbstractReliable estimates of future changes in extreme weather phenomena, such as tropical cyclone maximum wind speeds, are critical for climate change impact assessments and the development of appropriate adaptation strategies. However, global and regional climate model outputs are often too coarse for direct use in these applications, with variables such as wind speed having truncated probability distributions compared to those of observations. This poses two problems: How can model-simulated variables best be adjusted to make them more realistic? And how can such adjustments be used to make more reliable predictions of future changes in their distribution?This study investigates North Atlantic tropical cyclone maximum wind speeds from observations (1950–2010) and regional climate model simulations (1995–2005 and 2045–55 at 12- and 36-km spatial resolutions). The wind speed distributions in these datasets are well represented by the Weibull distribution, albeit with different scale and shape parameters.A power-law transfer function is used to recalibrate the Weibull variables and obtain future projections of wind speeds. Two different strategies, bias correction and change factor, are tested by using 36-km model data to predict future 12-km model data (pseudo-observations). The strategies are also applied to the observations to obtain likely predictions of the future distributions of wind speeds. The strategies yield similar predictions of likely changes in the fraction of events within Saffir–Simpson categories—for example, an increase from 21% (1995–2005) to 27%–37% (2045–55) for category 3 or above events and an increase from 1.6% (1995–2005) to 2.8%–9.8% (2045–55) for category 5 events.

Optimum order quantity with time lag and truncated distribution

This paper investigates the effect of inventory-level dependent demand of the displayed stock in the single item inventory model. It is supposed that the inventory-level dependent demand operates under the inventory received by the retailer in the beginning of the period and the time lag described between the display of the stock and customer’s response to the inventory. Using truncated probability distributions, we derive an optimum order quantity which should be ordered to maximize the expected profit.

A hybrid reliability model for structures with truncated probability distributions

In traditional reliability analysis, the uncertain parameters are generally treated by some ideal probability distributions with infinite tails, which, however, seems inconsistent with the practical situations as nearly all the uncertain parameters in engineering structures will get their values within a limited interval. To eliminate such an inconsistence and thereby improve the precision of the reliability analysis, the truncated probability distributions are then employed to quantify the uncertainty in this paper, and a corresponding reliability analysis method is developed. Two cases of positional relations are summarized for the uncertainty domain and the failure surface according to whether their intersection set is non-empty or empty. The probability and non-probability convex model methods are employed to deal with these two cases, respectively, and based on it, a hybrid reliability model is then constructed for truncated distribution problems. An efficient approach is also provided to distinguish these two positional relations and thereby determine which one of the probability and non-probability methods should be used when computing a real hybrid reliability. Five numerical examples are investigated to demonstrate the effectiveness of the present method.

Technique of solving a verification measurement problem on the basis of truncated distribution functions

A technique for a posteriori calculation of the characteristics of the basic error of measuring instruments from the data of a verification protocol and based on the use of truncated probability distributions is described.

Probabilistic approach to growth and detection of a truncated distribution of initial crack lengths based on Paris' law

A method for incorporating probabilistic considerations into fatigue life prognosis based on experimental information for Paris' law is presented in this article. A truncated probability distribution of initial crack lengths is introduced to obviate a complication of the use of Paris' law. This formulation allows the calculation of several probabilities for various values of the truncation length, including the probability of the existence of a crack larger than a predetermined critical crack length and the probability of a crack in a prescribed domain of crack lengths, and the effect of an inspection on these probabilities. A probabilistic consideration for the fact that the Paris' law parameters are not constants but distributions is also addressed using a stochastic version of Paris' law and a Monte Carlo simulation. Finally, a novel Bayesian approach which highlights the effect of probability of detection, critical crack length, and applied stress versus the number of elapsed fatigue cycles is presented and ramifications explored. This article provides insight on how various factors affect diagnosis and prognosis in a probabilistic manner.

10.1007/s11268-008-1003-0

The possibility of applying unilaterally truncated probability distributions of minimal water flow is considered. Relationships between moment estimates of truncated and full distributions are considered for the case of normal and gamma distributions.

Application of the theory of truncated probability distributions to studying minimal river runoff: Normal and gamma distributions

The possibility of applying unilaterally truncated probability distributions of minimal water flow is considered. Relationships between moment estimates of truncated and full distributions are considered for the case of normal and gamma distributions.

Dados climáticos simulados e produtividade potencial do milho

O objetivo deste trabalho foi avaliar uma metodologia para estimar a produtividade potencial da cultura do milho de acordo com valores médios diários de temperatura do ar e radiação solar, utilizando procedimento estocástico. Valores registrados da temperatura média diária do ar durante 86 anos e da radiação solar global diária durante 25 anos, foram fornecidos pela Estação Agrometeorológica de Piracicaba (Esalq/USP). Valores correspondentes à produtividade potencial foram simulados 1.000 vezes, em cada data de semeadura considerada (15/10 - época normal; 15/2 - safrinha; e 15/8 - safra de inverno). Foram considerados dois casos na distribuição de probabilidade normal truncada (valores extremos: média - 1,96 desvio-padrão e média + 1,96 desvio-padrão): temperatura média diária variável e radiação solar global diária constante, e temperatura média diária constante e radiação solar global diária variável. A metodologia de estimação permite definir a ordem de grandeza da produtividade potencial de milho a determinada localidade, com base nos dados de temperatura e radiação solar. O procedimento estocástico proposto permite associar a produtividade potencial de milho a determinada probabilidade.

Note on y-truncation: A simple approach to generating bounded distributions for environmental applications

It may sometimes be desirable to introduce bounds into probability distributions to formalise the presence of upper or lower physical limits to data to which the distribution has been applied. For example, an upper bound in raindrop sizes might be represented by introducing an upper bound to an exponential drop-size distribution. However, the standard method of truncating unbounded probability distributions yields distributions with non-zero probability density at the resulting bounds. In reality it is likely that physical bounding processes in nature increase in intensity as the bound is approached, causing a progressive decline in observation relative frequency to zero at the bound. Truncation below a y-axis point is proposed as a simple alternative means of creating more natural truncated probability distributions for application to data of this type. The resulting “ y-truncated” distributions have similarities with the traditional truncated distributions but probability densities have the desirable feature of always declining to zero at the bounds. In addition, the y-truncation approach can also serve in its own right as a means of creating a rich new class of bounded probability distributions when transformations of y-truncated distributions are included.

PROBABILISTIC DURABILITY PREDICTION OF EXISTING BUILDING ELEMENTS

An effect of service and proof actions on probabilistic reliability (serviceability, safety and durability) of building elements (components and members) of existing enclosure and bearing structures is under consideration. Time‐dependent models for reliability assessment of elements under sustained variable and multicycle actions are presented. Revised reliability indices of existing elements exposed to service permanent and variable actions are discussed. It is recommended to assess the long‐term reliability index of elements taking into account the effect of latent defects. Truncated probability distributions of physical‐mechanical resistances of elements and an effect of their latent defects on reliability index assessment are taken into account. Methodological peculiarities of durability prediction of elements and avoiding unfounded premature repairs or replacements are analysed. The applied illustration of the presented method on the probabilistic reliability prediction of deteriorating concrete covers is demonstrated.

Probabilistic durability prediction of existing building elements

Abstract An effect of service and proof actions on probabilistic reliability (serviceability, safety and durability) of building elements (components and members) of existing enclosure and bearing structures is under consideration. Time‐dependent models for reliability assessment of elements under sustained variable and multicycle actions are presented. Revised reliability indices of existing elements exposed to service permanent and variable actions are discussed. It is recommended to assess the long‐term reliability index of elements taking into account the effect of latent defects. Truncated probability distributions of physical‐mechanical resistances of elements and an effect of their latent defects on reliability index assessment are taken into account. Methodological peculiarities of durability prediction of elements and avoiding unfounded premature repairs or replacements are analysed. The applied illustration of the presented method on the probabilistic reliability prediction of deteriorating conc...

Fisher's information measures and truncated normal distributions (II)

The aim of this paper is to give some properties for the Fisher
 information measure when a random variable \(X\) follows a truncated
 probability distribution. A truncated probability distribution
 can be regarded as a conditional probability distribution, in the
 sense that if \(X\) has an unrestricted distribution with the
 probability density function \(f(x), \) then \(f_{a\leftrightarrow
 b}(x)\) is the probability density function which governs the
 behavior of \(X\), subject to the condition that \(X\) is known to lie
 in \([a,b]\).

Modelling of optimal specification regions

Design of screening procedures for industrial processes involves a decision-making strategy to select optimal specification regions under a 100% inspection scheme. Although researchers and practitioners have proposed a multitude of screening procedures under various assumptions, they have not thoroughly considered nor accurately captured outgoing product quality. This paper presents an optimization model for selecting optimal specification regions based on minimizing total cost. A defining aspect of this paper is the use of a truncated probability distribution to model the outgoing product distribution. Consequently, this paper proposes an enhanced modelling framework for designing screening procedures. A numerical example is presented to illustrate the optimization model.

Modelling of non-linear bar stochastical systems

Simple and practical analysis of probabilistic safety indexes of nonlinear bar systems is under consideracion.The nodal epizodic loading of systems and the left-side truncated probability distribution curves of their member resistances are taken into account. The analysis of long term member safety is based on dynamic models of stochastical sequence of its performance function. The evaluation of member safety indexes by the methods of cumulative coefficient of correlation and limit episodic action effects is presented.