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Hajime Murakami - One of the best experts on this subject based on the ideXlab platform.

  • Table1_Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.XLSX
    2019
    Co-Authors: Kazuhisa Takemura, Hajime Murakami
    Abstract:

    A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a Geometric Distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a Geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 − k log p)−1. Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a Geometric Distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

  • Image1_Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.TIFF
    2019
    Co-Authors: Kazuhisa Takemura, Hajime Murakami
    Abstract:

    A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a Geometric Distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a Geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 − k log p)−1. Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a Geometric Distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

  • probability weighting functions derived from hyperbolic time discounting psychophysical models and their individual level testing
    Frontiers in Psychology, 2016
    Co-Authors: Kazuhisa Takemura, Hajime Murakami
    Abstract:

    A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a Geometric Distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a Geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a Geometric Distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

Gauss M Cordeiro - One of the best experts on this subject based on the ideXlab platform.

  • a new lifetime model with variable shapes for the hazard rate
    Brazilian Journal of Probability and Statistics, 2017
    Co-Authors: Ahmed Z Afify, Gauss M Cordeiro, Nadeem Shafique Butt, Edwin M M Ortega, Adriano K Suzuki
    Abstract:

    We define and study a new generalization of the complementary Weibull Geometric Distribution introduced by Tojeiro et al. (J. Stat. Comput. Simul. 84 (2014) 1345–1362). The new lifetime model is referred to as the Kumaraswamy complementary Weibull Geometric Distribution and includes twenty three special models. Its hazard rate function can be constant, increasing, decreasing, bathtub and unimodal shaped. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, generating and quantile functions, Renyi entropy, mean residual life and mean inactivity time are derived. The method of maximum likelihood is used for estimating the model parameters. We provide some simulation results to assess the performance of the proposed model. Two applications to real data sets show the flexibility of the new model compared with some nested and non-nested models.

  • the exponentiated log logistic Geometric Distribution dual activation
    Communications in Statistics-theory and Methods, 2016
    Co-Authors: Natalie Veronika Rondinel Mendoza, Edwin M M Ortega, Gauss M Cordeiro
    Abstract:

    ABSTRACTThe log-logistic Distribution is commonly used to model lifetime data. We propose a wider Distribution, named the exponentiated log-logistic Geometric Distribution, based on a double activation approach. We obtain the quantile function, ordinary moments, and generating function. The method of maximum likelihood is used to estimate the model parameters. We propose a new extended regression model based on the logarithm of the exponentiated log-logistic Geometric Distribution. This regression model can be very useful in the analysis of real data and could provide better fits than other special regression models. The potentiality of the new models is illustrated by means of two applications to real lifetime data sets.

  • the beta weibull Geometric Distribution
    Statistics, 2013
    Co-Authors: Gauss M Cordeiro, Giovana O Silva, Edwin M M Ortega
    Abstract:

    We propose a new Distribution, the so-called beta-Weibull Geometric Distribution, whose failure rate function can be decreasing, increasing or an upside-down bathtub. This Distribution contains special sub-models the exponential Geometric [K. Adamidis and S. Loukas, A lifetime Distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42], beta exponential [S. Nadarajah and S. Kotz, The exponentiated type Distributions, Acta Appl. Math. 92 (2006), pp. 97–111; The beta exponential Distribution, Reliab. Eng. Syst. Saf. 91 (2006), pp. 689–697], Weibull Geometric [W. Barreto-Souza, A.L. de Morais, and G.M. Cordeiro, The Weibull-Geometric Distribution, J. Stat. Comput. Simul. 81 (2011), pp. 645–657], generalized exponential Geometric [R.B. Silva, W. Barreto-Souza, and G.M. Cordeiro, A new Distribution with decreasing, increasing and upside-down bathtub failure rate, Comput. Statist. Data Anal. 54 (2010), pp. 935–944; G.O. Silva, E.M.M. Ortega, and G.M. Cordeiro, The beta modified Weibu...

  • the weibull Geometric Distribution
    Journal of Statistical Computation and Simulation, 2011
    Co-Authors: Wagner Barretosouza, Alice Lemos De Morais, Gauss M Cordeiro
    Abstract:

    For the first time, we propose the Weibull-Geometric (WG) Distribution which generalizes the extended exponential-Geometric (EG) Distribution introduced by Adamidis et al. [K. Adamidis, T. Dimitrakopoulou, and S. Loukas, On a generalization of the exponential-Geometric Distribution, Statist. Probab. Lett. 73 (2005), pp. 259–269], the exponential-Geometric Distribution discussed by Adamidis and Loukas [K. Adamidis and S. Loukas, A lifetime Distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42] and the Weibull Distribution. We derive many of its standard properties. The hazard function of the EG Distribution is monotone decreasing, but the hazard function of the WG Distribution can take more general forms. Unlike the Weibull Distribution, the new Distribution is useful for modelling unimodal failure rates. We derive the cumulative Distribution and hazard functions, moments, density of order statistics and their moments. We provide expressions for the Renyi and Shannon entrop...

  • the weibull Geometric Distribution
    arXiv: Methodology, 2008
    Co-Authors: Wagner Barretosouza, Alice Lemos De Morais, Gauss M Cordeiro
    Abstract:

    In this paper we introduce, for the first time, the Weibull-Geometric Distribution which generalizes the exponential-Geometric Distribution proposed by Adamidis and Loukas (1998). The hazard function of the last Distribution is monotone decreasing but the hazard function of the new Distribution can take more general forms. Unlike the Weibull Distribution, the proposed Distribution is useful for modeling unimodal failure rates. We derive the cumulative Distribution and hazard functions, the density of the order statistics and calculate expressions for its moments and for the moments of the order statistics. We give expressions for the R\'enyi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an algorithm EM (Dempster et al., 1977; McLachlan and Krishnan, 1997) is provided for estimating the parameters. We obtain the information matrix and discuss inference. Applications to real data sets are given to show the flexibility and potentiality of the proposed Distribution.

Krzysztof Podgorski - One of the best experts on this subject based on the ideXlab platform.

  • Distributional properties of the negative binomial levy process
    Probability and Mathematical Statistics; 29(Fasc. 1) pp 43-71 (2009), 2009
    Co-Authors: Tomasz J Kozubowski, Krzysztof Podgorski
    Abstract:

    The Geometric Distribution leads to a Levy process parameterized by the probability of success. The resulting negative binomial process (NBP) is a purely jump and non-decreasing process with general negative binomial marginal Distributions. We review various stochastic mechanisms leading to this process, and study its Distributional structure. These results enable us to establish strong convergence of the NBP in the supremum norm to the gamma process, and lead to a straightforward algorithm for simulating sample paths.We also include a brief discussion of estimation of the NPB parameters, and present an example from hydrology illustrating possible applications of this model. (Less)

  • a bivariate levy process with negative binomial and gamma marginals
    Journal of Multivariate Analysis, 2008
    Co-Authors: Tomasz J Kozubowski, Anna K. Panorska, Krzysztof Podgorski
    Abstract:

    The joint Distribution of X and N, where N has a Geometric Distribution and X is the sum of N IID exponential variables (independent of N), is infinitely divisible. This leads to a bivariate Levy process {(X(t),N(t)),t>=0}, whose coordinates are correlated negative binomial and gamma processes. We derive basic properties of this process, including its covariance structure, representations, and stochastic self-similarity. We examine the joint Distribution of (X(t),N(t)) at a fixed time t, along with the marginal and conditional Distributions, joint integral transforms, moments, infinite divisibility, and stability with respect to random summation. We also discuss maximum likelihood estimation and simulation for this model.

  • a multivariate and asymmetric generalization of laplace Distribution
    Computational Statistics, 2000
    Co-Authors: Tomasz J Kozubowski, Krzysztof Podgorski
    Abstract:

    Consider a sum of independent and identically distributed random vectors with finite second moments, where the number of terms has a Geometric Distribution independent of the summands. We show that the class of limiting Distributions of such random sums, as the number of terms converges to infinity, consists of multivariate asymmetric Distributions that are natural generalizations of univariate Laplace laws. We call these limits multivariate asymmetric Laplace laws. We give an explicit form of their multidimensional densities and show representations that effectively facilitate computer simulation of variates from this class. We also discuss the relation to other formerly considered classes of Distributions containing Laplace laws.

Vicente G Cancho - One of the best experts on this subject based on the ideXlab platform.

  • the complementary exponential Geometric Distribution model properties and a comparison with its counterpart
    Computational Statistics & Data Analysis, 2011
    Co-Authors: Francisco Louzada, Mari Roman, Vicente G Cancho
    Abstract:

    In this paper, we proposed a new two-parameter lifetime Distribution with increasing failure rate, the complementary exponential Geometric Distribution, which is complementary to the exponential Geometric model proposed by Adamidis and Loukas (1998). The new Distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed Distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential Geometric Distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches.

Francisco Louzada - One of the best experts on this subject based on the ideXlab platform.

  • different estimation procedures for the parameters of the extended exponential Geometric Distribution for medical data
    Computational and Mathematical Methods in Medicine, 2016
    Co-Authors: Francisco Louzada, Pedro L Ramos, Gleici Da Silva Castro Perdona
    Abstract:

    We have considered different estimation procedures for the unknown parameters of the extended exponential Geometric Distribution. We introduce different types of estimators such as the maximum likelihood, method of moments, modified moments, L-moments, ordinary and weighted least squares, percentile, maximum product of spacings, and minimum distance estimators. The different estimators are compared by using extensive numerical simulations. We discovered that the maximum product of spacings estimator has the smallest mean square errors and mean relative estimates, nearest to one, for both parameters, proving to be the most efficient method compared to other methods. Combining these results with the good properties of the method such as consistency, asymptotic efficiency, normality, and invariance we conclude that the maximum product of spacings estimator is the best one for estimating the parameters of the extended exponential Geometric Distribution in comparison with its competitors. For the sake of illustration, we apply our proposed methodology in two important data sets, demonstrating that the EEG Distribution is a simple alternative to be used for lifetime data.

  • the complementary exponential Geometric Distribution model properties and a comparison with its counterpart
    Computational Statistics & Data Analysis, 2011
    Co-Authors: Francisco Louzada, Mari Roman, Vicente G Cancho
    Abstract:

    In this paper, we proposed a new two-parameter lifetime Distribution with increasing failure rate, the complementary exponential Geometric Distribution, which is complementary to the exponential Geometric model proposed by Adamidis and Loukas (1998). The new Distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed Distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential Geometric Distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches.