Location parameter
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On the Three-Parameter Weibull Distribution Shape Parameter Estimation Open
The Weibull distribution has received much interest in reliability theory. The well-known maximum likelihood estimators (MLE) of this fam ily are not available in closed form expression. In this work, we propose a consistent and closed for…
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Improvement of hydrological model calibration by selecting multiple parameter ranges Open
The parameters of hydrological models are usually calibrated to achieve good performance, owing to the highly non-linear problem of hydrology process modelling. However, parameter calibration efficiency has a direct relation with parameter…
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Reaction Times and other Skewed Distributions Open
To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tende…
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Robust isochron calculation Open
The standard classical statistics approach to isochron calculation assumes that the distribution of uncertainties on the data arising from isotopic analysis is strictly Gaussian. This effectively excludes datasets that have more scatter fr…
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Reaction times and other skewed distributions: problems with the mean and the median Open
To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tende…
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Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions Open
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 di…
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On the automatic selection of the tuning parameter appearing in certain families of goodness-of-fit tests Open
The situation, common in the current literature, is that of a whole family of location-scale/scale invariant test statistics, indexed by a parameter $\\lambda\\in\\Lambda$, is available to test the goodness of fit of $F$, the underlying di…
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Reaction times and other skewed distributions: problems with the mean and the median Open
To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tende…
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On designing a new cumulative sum Wilcoxon signed rank chart for monitoring process location Open
In this paper, ranked set sampling is used for developing a non-parametric location chart which is developed on the basis of Wilcoxon signed rank statistic. The average run length and some other characteristics of run length are used as th…
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A new log-location regression model: estimation, influence diagnostics and residual analysis Open
We introduce a log-linear regression model based on the odd log-logistic generalized half-normal distribution [7 G.M. Cordeiro, M. Alizadeh, R.R. Pescim, and E.M.M. Ortega, The odd log-logistic generalized half-normal lifetime distribution…
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Impacts of Max-Stable Process Areal Exceedance Calculations to Study Area Sampling Density, Surface Network Precipitation Gage Extent and Density, and Model Fitting Method Open
Max-stable process (MSP) models can be fit to data collected over a spatial domain to estimate areal-based exceedances while accounting for spatial dependence in extremes. They have theoretical grounding within the framework of extreme val…
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Admissible Bayes equivariant estimation of location vectors for spherically symmetric distributions with unknown scale Open
This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form $f(x,u)=\\eta ^{(p+n)/2}f(\\eta \\{\\|x-\\theta \\|^{2}+\\|u\\…
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A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution Open
We considered the Bayesian analysis of a shape parameter of the Weibull-Exponential distribution in this paper. We assumed a class of non-informative priors in deriving the corresponding posterior distributions. In particular, the …
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MAD (about median) vs. quantile-based alternatives for classical standard deviation, skewness, and kurtosis Open
In classical probability and statistics, one computes many measures of interest from mean and standard deviation. However, mean, and especially standard deviation, are overly sensitive to outliers. One way to address this sensitivity is by…
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On predictive density estimation for location families under integrated absolute error loss Open
This paper is concerned with estimating a predictive density under integrated absolute error ($L_{1}$) loss. Based on a spherically symmetric observable $X\\sim p_{X}(\\Vert x-\\mu\\Vert^{2})$, $x,\\mu \\in \\mathbb{R}^{d}$, we seek to est…
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Parameter estimation of geographically weigthed multivariate Poisson regression Open
Geographically Weighted Multivariate Poisson Regression (GWMPR) is a statistical technique on spatial data which is used to modelling of relationships between two or more response variables (Poisson distribution) and one or more independen…
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Temporal and spatial variations in annual rainfall distribution in Erbil province Open
This study aimed to determine the best fit probability distribution of annual maximum rainfall using data from nine stations within Erbil province using different statistical analyses. Nine commonly used probability distribution functions,…
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Distributions of Birkeland Current Density Observed by AMPERE are Heavy‐Tailed or Long‐Tailed Open
We analyze probability distributions of Birkeland current densities measured by the Active Magnetosphere and Planetary Electrodynamics Response Experiment. We find that the distributions are leptokurtic rather than normal and they are some…
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Bayes Estimation of Parameter of Laplace Distribution Under a New LINEX-Based Loss Function Open
Loss function is one of the most topics in Bayesian analysis. The aim of this paper is to study the estimation of the shape parameter of Laplace distribution using Bayesian technique under a new loss function, which is a compound function …
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Information–Theoretic Aspects of Location Parameter Estimation under Skew–Normal Settings Open
In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean’s estimation. The class of skew–normal distributions is considered, given their flexibility for modeli…
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Estimation of common location parameter of several heterogeneous exponential populations based on generalized order statistics Open
In this article, several independent populations following exponential distribution with common location parameter and unknown and unequal scale parameters are considered. From these populations, several independent samples of generalized …
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Fisher SAM: Information Geometry and Sharpness Aware Minimisation Open
Recent sharpness-aware minimisation (SAM) is known to find flat minima which is beneficial for better generalisation with improved robustness. SAM essentially modifies the loss function by reporting the maximum loss value within the small …
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Robust estimation of the location and the scale parameters of shifted Gompertz distribution Open
In this study, we consider the estimation of the location parameter and the scale parameter of the shifted Gompertz (SG) distribution. We obtain the closed form estimators of these parameters by using the modified maximum likelihood (MML) …
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Spatial dependence and space-time trend in extreme events:Space-time trend in extremes Open
he statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the mar…
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Improvement of hydrological model calibration by selecting multiple parameter ranges Open
The parameters of hydrological models are usually calibrated to achieve a good performance of the model, owing to the highly non-linear problem of hydrology process modelling. However, parameter calibration efficiency has a direct relation…
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A New Extended Mixture Skew Normal Distribution, With Applications Open
One of the most important property of the mixture normal distributions-model is its flexibility to accommodate various types of distribution functions (df's). We show that the mixture of the skew normal distribution and its reverse, after …
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A Two-Stage Maximum Entropy Prior of Location Parameter with a Stochastic Multivariate Interval Constraint and Its Properties Open
This paper proposes a two-stage maximum entropy prior to elicit uncertainty regarding a multivariate interval constraint of the location parameter of a scale mixture of normal model. Using Shannon’s entropy, this study demonstrates how the…
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M-Estimations of Shape and Scale Parameters by Order Statistics in Least Informative Distributions on q-deformed logarithm Open
The maximum logq likelihood estimation (MLqE) method is used to estimate robustly parameters recently. In robust estimation method, the least informative distribution (LID) proposed by Huber is a convex combination of two probability densi…
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Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions Open
In this article, we propose nonparametric tests for simultaneously testing equality of location and scale parameters of two multivariate distributions by using nonparametric combination theory. Our approach is to combine the data depth bas…
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Tail bounds for empirically standardized sums Open
Exponential tail bounds for sums play an important role in statistics, but the example of the t-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns ou…