Half-normal Distribution Research Articles

Generalized half-normal distribution: Model and properties

Generalized half-normal distribution: Model and properties

Bayesian A- and D-optimal designs for gamma regression model with inverse link function

ABSTRACTBayesian optimal designs have received increasing attention in recent years, especially in biomedical and clinical trials. Bayesian design procedures can utilize the available prior information of the unknown parameters so that a better design can be achieved. With this in mind, this article considers the Bayesian A- and D-optimal designs of the two- and three-parameter Gamma regression model. In this regard, we first obtain the Fisher information matrix of the proposed model and then calculate the Bayesian A- and D-optimal designs assuming various prior distributions such as normal, half-normal, gamma, and uniform distribution for the unknown parameters. All of the numerical calculations are handled in R software. The results of this article are useful in medical and industrial researches.

Estimation for constant-stress accelerated life test from generalized half-normal distribution

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

A generalization of the half-normal distribution

In this paper we introduce an extension of the half-normal distribution in order to model a great variety of non-negative data. Its hazard rate function can be decreasing or increasing, depending on its parameters. Some properties of this new distribution are presented. For example, we give a general expression for the moments and a stochastic representation. Also, the cumulative distribution function, the hazard rate function, the survival function and the quantile function can be easily evaluated. Maximum likelihood estimators can be computed by using numerical procedures. Finally, a real-life dataset has been presented to illustrate its applicability.

Variable Limits and Control Charts Based on the Half Normal Distribution

Abstract The well-known variable control charts for mean and range of sub-groups for the half normal distribution were constructed by three different approaches. One from the first principles of using percentiles of the sampling distribution of the sample mean and sample range, the second from Shewhart control limits, and the third approach was a skewness correction procedure depending on the skewness coefficient. The coverage probabilities of the three different approaches were computed through simulation and compared.

The extended generalized half-normal distribution

Fatigue is a structural damage which occurs when a material is exposed to stress and tension fluctuations. We propose and study the extended generalized half-normal distribution for modeling skewed fatigue life data. The new model contains as special cases the half-normal and generalized half-normal (Comm. Statist. Theory Methods 37 (2008) 1323–1337) distributions. Various of its structural properties are derived, including the density function, moments, quantile and generating functions, mean deviations and order statistics. We investigate maximum likelihood estimation of the model parameters. An application illustrates the potentiality of the new distribution.

The Geometric Power Half-Normal Regression Model with Cure Rate

In this paper we consider the geometric cure rate model defined in [16], using for $S_0(\cdot)$, the survival function of carcinogenic cells, an extension of the half-normal distribution based on the distribution of the maximum of a random sample. The implementation of maximum likelihood estimation for the model parameters is discussed and, nally, the model is fitted to a real database (Melanoma data set), and comparisons are performed with alternatives to the new $S_0(\cdot)$ .

Exploring the distribution for the estimator of Rosenthal's ‘fail-safe’ number of unpublished studies in meta-analysis

ABSTRACTThe present article discusses the statistical distribution for the estimator of Rosenthal's ‘file-drawer’ number NR, which is an estimator of unpublished studies in meta-analysis. We calculate the probability distribution function of NR. This is achieved based on the central limit theorem and the proposition that certain components of the estimator NR follow a half-normal distribution, derived from the standard normal distribution. Our proposed distributions are supported by simulations and investigation of convergence.

A study of generalized normal distributions

ABSTRACTIn this work, first some distributional properties of extended two-piece skew normal distributions are presented. Next we revisit the special case, that is two-piece skew normal distributions. Then two distributions related to two-piece skew normal distributions are studied. More precisely, we give some properties about generalized half normal distributions as well as a generalized Cauchy distribution. Finally, we discuss the distributions of linear combinations of two independent skew normal random variables.

ROC Curve Estimation Using the Combination of Generalized Half Normal and Weibull Distributions

Receiver Operating Characteristic (ROC) Curve is an important classification tool to classify the subjects into one of the two populations. In literature, many ROC models exist based on bi-distributional assumptions with location and scale parameters. The proposed ROC model considers Generalized Half Normal and Weibull distributions with shape and scale parameters. Further, area under the curve and Kullback–Leibler divergence are derived to observe the discriminatory ability of a test and the proximity between two densities. The proposed methodology is supported using simulation studies and a real data set (SAPS III).

The odd log-logistic generalized half-normal lifetime distribution: Properties and applications

ABSTRACTCooray and Ananda (2008) pioneered a lifetime model commonly used in reliability studies. Based on this distribution, we propose a new model called the odd log-logistic generalized half-normal distribution for describing fatigue lifetime data. Various of its structural properties are derived. We discuss the method of maximum likelihood to fit the model parameters. For different parameter settings and sample sizes, some simulation studies compare the performance of the new lifetime model. It can be very useful, and its superiority is illustrated by means of a real dataset.

Generalized gamma approximation with rates for urns, walks and trees

We study a new class of time inhomogeneous P\'olya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein's method combined with characterizing the generalized gamma limiting distributions as fixed points of distributional transformations related to the equilibrium distributional transformation from renewal theory. We identify special cases of these urn models in recursive constructions of random walk paths and trees, yielding rates of convergence for local time and height statistics of simple random walk paths, as well as for the size of random subtrees of uniformly random binary and plane trees.

A new log-location regression model: estimation, influence diagnostics and residual analysis

ABSTRACTWe introduce a log-linear regression model based on the odd log-logistic generalized half-normal distribution [7]. Some of its structural properties including explicit expressions for the density function, quantile and generating functions and ordinary moments are derived. We estimate the model parameters by the maximum likelihood method. For different parameter settings, proportion of censoring and sample size, some simulations are performed to investigate the behavior of the estimators. We derive the appropriate matrices for assessing local influence diagnostics on the parameter estimates under different perturbation schemes. We also define the martingale and modified deviance residuals to detect outliers and evaluate the model assumptions. In addition, we demonstrate that the extended regression model can be very useful in the analysis of real data and provide more realistic fits than other special regression models. The potentiality of the new regression model is illustrated by means of a real data set.

Double Acceptance Sampling Plan for Time-Truncated Life Tests Based on Half Normal Distribution

AbstractIn this work, we investigate a double acceptance sampling plan (DASP) based on truncated life tests when the lifetime of a product follows the half normal distribution. By fixing the consumer’s confidence level, the minimum sample sizes of the first and second samples needful to assert the specified mean life are calculated. The operating characteristic values and the minimum ratios of the mean life to the specified life are also analyzed. Several important tables are provided and a numerical example is given to illustrate the results.

Surveying Two Endangered Primate Species (Alouatta palliata aequatorialis and Cebus aequatorialis) in the Pacoche Marine and Coastal Wildlife Refuge, West Ecuador

Accurate information on the distribution, demography, and conservation status of endangered populations in threatened habitats are essential to provide the basis for conservation actions and management plans. Neglect of western Ecuador by biologists has resulted in a paucity of information of primate populations in the region. Capuchins (Cebus spp.) and howlers (Alouatta sp.) occur in the Tumbes–Choco–Magdalena hotspot along the Pacific coast. We conducted the first primate survey in Pacoche Marine and Coastal Wildlife Refuge, one of the few protected areas in western Ecuador. Although the Pacoche refuge is protected, illegal activities inside the area include slash-and-burn agriculture and natural resource extraction. We surveyed 18 1-km transects within the protected area between April and July 2012 to evaluate the effects of anthropogenic disturbance and habitat characteristics on population densities of the Critically Endangered Ecuadorian white-fronted capuchin (Cebus aequatorialis) and the Vulnerable mantled howler (Alouatta palliata aequatorialis). We confirmed the presence of C. aequatorialis through direct observation on three occasions outside transects. The low detection rate of C. aequatorialis underscores the need for immediate conservation action for this species. Using a hierarchical distance sampling model, we predicted group size as a proxy of probability of detection and found that canopy cover explained group density of A. p. aequatorialis, following a half-normal distribution. We estimated the mean density of A. p. aequatorialis as 12.4 ind./km2 and the total population to be 621.5 individuals. The correlation between the density of A. p. aequatorialis and canopy cover underlines the need to preserve the remaining forest and its connectivity. Our results also highlight the importance of including vegetation structure in primate censuses.

Commentary: Unlearning implicit social biases during sleep

Commentary: Unlearning implicit social biases during sleep

Unbiased Estimation for the General Half-Normal Distribution

This work proposes unbiased estimators for the parameters of the general half-normal distribution that exhibit a better performance than the estimators based on maximum likelihood proposed in the literature. From these estimators, large sample confidence sets are also derived.

A spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers

By blending seminal literature on non-spatial stochastic frontier models with key contributions to spatial econometrics we develop a spatial autoregressive (SAR) stochastic frontier for panel data. The specification of the SAR frontier allows efficiency to vary over time and across the cross-sections. Efficiency is calculated from a composed error structure by assuming a half-normal distribution for inefficiency. The SAR frontier is estimated using maximum likelihood methods taking into account the endogenous SAR variable. The application of the estimator to an aggregate production frontier for European countries highlights, among other things, the asymmetry between efficiency spillovers to and from a country.

Two stage group acceptance sampling plan for half normal percentiles

In this paper, a time truncated life test based on two stage group acceptance sampling plan for the percentile lifetime following half-normal distribution is proposed. The optimal parameters for the proposed plan are determined such that both producer’s and consumer’s risks are satisfied simultaneously for the given experimentation time and sample size. The efficiency of the proposed sampling plan is discussed in terms of average sample number with the existing sampling plan. The proposed sampling plan is explained with the help of industrial examples.

Generalized variable method inference for the location parameter of the general half-normal distribution

This paper considers the development of inferential techniques based on the generalized variable method (GV-Method) for the location parameter of the general half-normal distribution. We are interested in hypothesis testing of, and interval estimation for, the location parameter. Body fat data, urinary excretion rate data, and simulated data are used to illustrate the application and to demonstrate the advantages of the proposed GV-Method over the large-sample method and the Bayesian method.