• Title/Summary/Keyword: Statistical Discrete Distribution

Search Result 66, Processing Time 0.026 seconds

A two-parameter discrete distribution with a bathtub hazard shape

  • Sarhan, Ammar M.
    • Communications for Statistical Applications and Methods
    • /
    • v.24 no.1
    • /
    • pp.15-27
    • /
    • 2017
  • This paper introduces a two-parameter discrete distribution based on a continuous two-parameter bathtub distribution. It is the only two-parameter discrete distribution that shows a bathtub-shaped hazard function. Some statistical properties of the distribution are discussed. Three different methods are used to estimate its two unknown parameters. The point estimators of the parameters have no closed form. The bootstrap method is used to estimate the distributions of these point estimators. Different approximations of the interval estimations for the two-parameters are discussed. Real data sets are analyzed to show how this distribution works in practice. A simulation study is performed to investigate the properties of the estimations obtained and compare their performances.

SOME PROPERTIES OF BIVARIATE GENERALIZED HYPERGEOMETRIC PROBABILITY DISTRIBUTIONS

  • Kumar, C. Satheesh
    • Journal of the Korean Statistical Society
    • /
    • v.36 no.3
    • /
    • pp.349-355
    • /
    • 2007
  • In this paper we study some important properties of the bivariate generalized hypergeometric probability (BGHP) distribution by establishing the existence of all the moments of the distribution and by deriving recurrence relations for raw moments. It is shown that certain mixtures of BGHP distributions are again BGHP distributions and a limiting case of the distribution is considered.

Simultaneous Estimation of Parameters from Power Series Distributions under Asymmetric Loss

  • Chung, Youn-Shik;Dipak K. Dey
    • Journal of the Korean Statistical Society
    • /
    • v.23 no.1
    • /
    • pp.151-166
    • /
    • 1994
  • Let $X_1, \cdot, X_p$ be p independent random variables, where each $X_i$ has a distribution belonging to one parameter discrete power series distribution. The problem is to simultaneously estimate the unknown parameters under an asymmetric loss. Several new classes of dominating estimators are obtained by solving certain difference inequality.

  • PDF

A Discrete Time Approximation Method using Bayesian Inference of Parameters of Weibull Distribution and Acceleration Parameters with Time-Varying Stresses (시변환 스트레스 조건에서의 와이블 분포의 모수 및 가속 모수에 대한 베이시안 추정을 사용하는 이산 시간 접근 방법)

  • Chung, In-Seung
    • Proceedings of the KSME Conference
    • /
    • 2008.11a
    • /
    • pp.1331-1336
    • /
    • 2008
  • This paper suggests a method using Bayesian inference to estimate the parameters of Weibull distribution and acceleration parameters under the condition that the stresses are time-dependent functions. A Bayesian model based on the discrete time approximation is formulated to infer the parameters of interest from the failure data of the virtual tests and a statistical analysis is considered to decide the most probable mean values of the parameters for reasoning of the failure data.

  • PDF

Independence test of a continuous random variable and a discrete random variable

  • Yang, Jinyoung;Kim, Mijeong
    • Communications for Statistical Applications and Methods
    • /
    • v.27 no.3
    • /
    • pp.285-299
    • /
    • 2020
  • In many cases, we are interested in identifying independence between variables. For continuous random variables, correlation coefficients are often used to describe the relationship between variables; however, correlation does not imply independence. For finite discrete random variables, we can use the Pearson chi-square test to find independency. For the mixed type of continuous and discrete random variables, we do not have a general type of independent test. In this study, we develop a independence test of a continuous random variable and a discrete random variable without assuming a specific distribution using kernel density estimation. We provide some statistical criteria to test independence under some special settings and apply the proposed independence test to Pima Indian diabetes data. Through simulations, we calculate false positive rates and true positive rates to compare the proposed test and Kolmogorov-Smirnov test.

Application of discrete Weibull regression model with multiple imputation

  • Yoo, Hanna
    • Communications for Statistical Applications and Methods
    • /
    • v.26 no.3
    • /
    • pp.325-336
    • /
    • 2019
  • In this article we extend the discrete Weibull regression model in the presence of missing data. Discrete Weibull regression models can be adapted to various type of dispersion data however, it is not widely used. Recently Yoo (Journal of the Korean Data and Information Science Society, 30, 11-22, 2019) adapted the discrete Weibull regression model using single imputation. We extend their studies by using multiple imputation also with several various settings and compare the results. The purpose of this study is to address the merit of using multiple imputation in the presence of missing data in discrete count data. We analyzed the seventh Korean National Health and Nutrition Examination Survey (KNHANES VII), from 2016 to assess the factors influencing the variable, 1 month hospital stay, and we compared the results using discrete Weibull regression model with those of Poisson, negative Binomial and zero-inflated Poisson regression models, which are widely used in count data analyses. The results showed that the discrete Weibull regression model using multiple imputation provided the best fit. We also performed simulation studies to show the accuracy of the discrete Weibull regression using multiple imputation given both under- and over-dispersed distribution, as well as varying missing rates and sample size. Sensitivity analysis showed the influence of mis-specification and the robustness of the discrete Weibull model. Using imputation with discrete Weibull regression to analyze discrete data will increase explanatory power and is widely applicable to various types of dispersion data with a unified model.

A Bayesian cure rate model with dispersion induced by discrete frailty

  • Cancho, Vicente G.;Zavaleta, Katherine E.C.;Macera, Marcia A.C.;Suzuki, Adriano K.;Louzada, Francisco
    • Communications for Statistical Applications and Methods
    • /
    • v.25 no.5
    • /
    • pp.471-488
    • /
    • 2018
  • In this paper, we propose extending proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured. Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. This proposal also allows for a realistic description of non-risk individuals, since individuals cured due to intrinsic factors (immunes) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. We put the proposed model in a Bayesian framework and use a Markov chain Monte Carlo algorithm for the computation of posterior distribution. A simulation study is conducted to assess the proposed model and the computation algorithm. We also discuss model selection based on pseudo-Bayes factors as well as developing case influence diagnostics for the joint posterior distribution through ${\psi}-divergence$ measures. The motivating cutaneous melanoma data is analyzed for illustration purposes.

Criterion of discrete unimodal mixtures (이산분포 혼합의 단봉성이 성립하기 위한 조건)

  • 최대우
    • The Korean Journal of Applied Statistics
    • /
    • v.8 no.1
    • /
    • pp.159-167
    • /
    • 1995
  • Considering special discrete distribution of exponential family as a sequence with respect to the points of support, the squence is unimodal in some sense. In this paper, we study under what condition the mixture of that discrete distribution with respect to a parameter is unimodal. We derive the maximal interval of the parameter in which each mixture of the discrete distribution such as Binomial and Poisson is always unimodal.

  • PDF

On Bounds for Moments of Unimodal Distributions

  • Sharma, R.;Bhandaria, R.
    • Communications for Statistical Applications and Methods
    • /
    • v.21 no.3
    • /
    • pp.201-212
    • /
    • 2014
  • We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

Multivariate Modified Discrete Distributions

  • Lingappaiah, G.S.
    • Journal of the Korean Statistical Society
    • /
    • v.15 no.1
    • /
    • pp.71-78
    • /
    • 1986
  • In this paper, multivariate discrete distribution is dealt with, where a set of r distinct counts are misreported as another set of r counts. First, the variance for the one variable marginal case is expressed in the form of an inverted parabola. Next, for the multivariate negative binomial case, elements of the covariance matrix are evaluated with reference to asymptotic distributions. Finally, for the same case of multivariate negative binomial, Bayesian estimates of the parameters and of the modification rates are provided.

  • PDF