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The plug-in predictor of the posterior mean of the canonical parameter minimizes the posterior mean of the Kullback-Leibler loss in the exponential family. We observe that the posterior mean under the reference prior implies an approximately unbiased estimator of a suitably chosen form of the parameter. In fact, amounts of bias are very small, even for small sample sizes. While special attention is placed on the case of the inverse Gaussian distribution, other familiar distributions are examined as well. Our results suggest that the posterior mean of the canonical parameter of an exponential family under the reference prior is a promising estimator. [ABSTRACT FROM AUTHOR]

In this paper, we study the autoregressive (AR) model with normal inverse Gaussian (NIG) innovations. The NIG distribution is semi heavy-tailed and is helpful in capturing the extreme observations present in the data. The expectation-maximization (EM) algorithm is used to estimate the parameters of the considered AR(p) model. The efficacy of the estimation procedure is shown on the simulated data for AR(2) and AR(1) models. A comparative study is presented, where the classical estimation algorithms are also incorporated, namely, Yule-Walker and conditional least squares methods along with EM method for model parameter estimation. In simulation study, the maximum likelihood estimation (MLE) of NIG distribution by EM algorithm and iterative Newton-Raphson method are also compared. The real-life applications of the introduced model are demonstrated on the NASDAQ stock market index data and US gasoline price data. The studies show that AR(1) model with NIG residuals is good fit for financial data with extreme values as well as for gasoline price data. [ABSTRACT FROM AUTHOR]

We develop an economic model of transitions in and out of employment. Heterogeneous workers switch employment status when the net benefit from working, a Brownian motion with drift, hits optimally chosen barriers. This implies that the duration of jobless spells for each worker has an inverse Gaussian distribution. We allow for arbitrary heterogeneity across workers and prove that the distribution of inverse Gaussian distributions is partially identified from the duration of two non-employment spells for each worker. We estimate the model using Austrian social security data and find that dynamic selection is a critical source of duration dependence. [ABSTRACT FROM AUTHOR]

Introduction: Although studies have evaluated the hospital cost of care associated with treating patients with COVID-19, there are no studies that compare the hospital cost of care among racial and ethnic groups based on detailed cost accounting data. The aims of this study were to provide a detailed description of the hospital costs of COVID-19 based on individual resources during the hospital stay and standardized costs that do not rely on inflation adjustment and evaluate the extent to which hospital total cost of care for patients with COVID-19 differs by race and ethnicity. Methods: This study used electronic medical record data from an urban academic medical center in Chicago, Illinois USA. Hospital cost of care was calculated using accounting data representing the cost of the resources used to the hospital (i.e., cost to the hospital, not payments). A multivariable generalized linear model with a log link function and inverse gaussian distribution family was used to calculate the average marginal effect (AME) for Black, White, and Hispanic patients. A second regression model further compared Hispanic patients by preferred language (English versus Spanish). Results: In our sample of 1,853 patients, the average adjusted cost of care was significantly lower for Black compared to White patients (AME = -$5,606; 95% confidence interval (CI), -$10,711 to -$501), and Hispanic patients had higher cost of care compared to White patients (AME = $8,539, 95% CI, $3,963 to $13,115). In addition, Hispanic patients who preferred Spanish had significantly higher cost than Hispanic patients who preferred English (AME = $11,866; 95% CI $5,302 to $18,431). Conclusion: Total cost of care takes into account both the intensity of the treatment as well as the duration of the hospital stay. Thus, policy makers and health systems can use cost of care as a proxy for severity, especially when looking at the disparities among different race and ethnicity groups. [ABSTRACT FROM AUTHOR]

This paper proposes a trajectory multi-Bernoulli filter applied to the superpositional sensor model for multi-target tracking in the presence of unknown measurement noise. This filter can provide a Multi-Bernoulli approximation of the posterior density on a set of alive trajectories at the current time step. We also provide a Gaussian mixture (GM) implementation of this filter, employing a mixture of Gaussian and inverse Wishart distributions to represent the combined state of measurement noise and target information. Subsequently, the variational Bayesian (VB) method is employed to approximate the posterior distribution, ensuring its form remains consistent with the prior distribution. This method is capable of directly generating trajectory estimates and can jointly estimate both multi-object tracking and measurement noise covariance. The performance of this algorithm is verified through simulation. Finally, a computationally more efficient L-scan approximation is provided. The simulation results indicate that the filter can achieve robust tracking performance, adapting to unknown measurement noise. [ABSTRACT FROM AUTHOR]

The Youden index is often used to measure the effectiveness of biomarkers and aids to find the optimal cutoff point. Since pooled specimens have been shown to be an effective cost-cutting technique, we proposed the exact inferential procedures for the Youden index and its associated cutoff point based on the pooled specimens under the gamma or the inverse Gaussian assumption. The generalized confidence intervals (GCIs) were proposed for the Youden index and its associated cutoff point. Monte Carlo simulations were used to assess the performance of the proposed GCIs. The simulation results show that the proposed GCIs outperformed existing methods such as the bootstrap- p CIs in terms of the coverage probability. Finally, the proposed procedures were illustrated by an example. [ABSTRACT FROM AUTHOR]

Recent studies have highlighted leptin, a key hormone that regulates energy intake and induces satiety, due to the worldwide prevalence of obesity. In this study, we analyzed plasma leptin measurements from 18 women with premenopausal obesity before and after bromocriptine treatment. By using underlying pulses recovered through deconvolution, we modeled the leptin secretory pulses as marked point processes and applied statistical distributions to evaluate the dynamics of leptin, including the interpulse intervals and amplitudes of the secretion. We fit the generalized inverse Gaussian and lognormal distributions to the intervals and the Gaussian, lognormal, and gamma distributions to the amplitudes of pulses. We evaluated the models' goodness of fit using statistical metrics including Akaike's information criterion, Kolmogorov-Smirnov plots, and quantile-quantile plots. Our evaluation results revealed the effectiveness of these statistical distributions in modeling leptin secretion. Although the lognormal and gamma distributions performed the best based on the metrics, we found all distributions capable of accurately modeling the timing of secretory events, leading us to a better understanding of the physiology of leptin secretion and providing a basis for leptin monitoring. In terms of pulse amplitude, the evaluation metrics indicated the gamma distribution as the most accurate statistical representation. We found no statistically significant effect of bromocriptine intake on the model parameters except for one distribution model. [ABSTRACT FROM AUTHOR]

AbstractThe financial market returns and daily range data often exhibit asymmetry and peak around the mean with heavier tails than normal distribution. To analyze the volatility dynamics of these financial time series using stochastic conditional range (SCR) models, the choice of conditional distribution for innovations has posed challenges. A suitably chosen distribution, which can capture stylized facts inherent in these data, particularly excess kurtosis, has been proven to be very useful. This study introduces a new parameterization for SCR models using an extended generalized inverse Gaussian distribution to incorporate the flexibility of choice of various marginal distributions to the innovations of the model. We discuss the theoretical properties of the proposed models and develop a maximum likelihood method based on efficient importance sampling to estimate the parameters of the proposed SCR models. The simulation results showed that the proposed estimation methodology performs well. Finally, the proposed models were used to analyze real datasets. [ABSTRACT FROM AUTHOR]

This paper deals with estimating the underlying parameter of a length-biased inverse Gaussian distribution, when the observations are prone to length-biased sampling. Length-biased sampling occurs when the observations of smaller lengths or dimensions are neglected from the sample. We focus on a particular type of sequential fixed-accuracy confidence interval for estimation purposes. This method proves to be both time and cost efficient as one is able to perform the estimation using an optimal number of observations according to some set criteria. We discuss the applicability of our proposed method with regards to estimating the cluster size of the "Eastern Tropical Pacific Dolphins", which are often vulnerable to length biasedness. [ABSTRACT FROM AUTHOR]

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators. [ABSTRACT FROM AUTHOR]

Let X be a random variable with finite second moment. We investigate the inequality: P { | X - E [ X ] | ≤ Var (X) } ≥ P { | Z | ≤ 1 } , where Z is a standard normal random variable. We prove that this inequality holds for many familiar infinitely divisible continuous distributions including the Laplace, Gumbel, Logistic, Pareto, infinitely divisible Weibull, Log-normal, Student's t and Inverse Gaussian distributions. Numerical results are given to show that the inequality with continuity correction also holds for some infinitely divisible discrete distributions. [ABSTRACT FROM AUTHOR]

The Youden index is often used to measure the effectiveness of biomarkers and aids to find the optimal cutoff point. Since pooled specimens have been shown to be an effective cost-cutting technique, we proposed the exact inferential procedures for the Youden index and its associated cutoff point based on the pooled specimens under the gamma or the inverse Gaussian assumption. The generalized confidence intervals (GCIs) were proposed for the Youden index and its associated cutoff point. Monte Carlo simulations were used to assess the performance of the proposed GCIs. The simulation results show that the proposed GCIs outperformed existing methods such as the bootstrap-$ p $ CIs in terms of the coverage probability. Finally, the proposed procedures were illustrated by an example.

This article presents a mixed Pareto model and examines its suitability for modeling non life insurance claim severity data sets which exhibit peculiar characteristics that cannot be captured by the Pareto distribution. Furthermore, we introduce regression specifications for both the mean and the dispersion parameters of the mixed Pareto model. Our main achievement is that we develop a novel Expectation-Maximization (EM) algorithm for finding the maximum likelihood (ML) estimates of the parameters of the mixed Pareto regression model which is used for demonstration purposes. Finally, a real-data application based on motor insurance claim size data is provided. [ABSTRACT FROM AUTHOR]

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches. [ABSTRACT FROM AUTHOR]

This article presents the problem of interval estimation of the mean, difference and ratio of means for zero-adjusted inverse Gaussian distributions. Confidence intervals of the mean are derived using signed log-likelihood, method of variance estimate recovery (MOVER), generalized variable, and Bayesian approaches. For two populations, we derive MOVER, generalized variable-based interval, and Bayesian intervals for the difference and ratio of means. We perform intensive simulations to compare the proposed confidence intervals of the function of parameters. Finally, illustrative examples are given using real data sets from different fields. [ABSTRACT FROM AUTHOR]

The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as P M 2.5 levels. The coefficient of variation is often used to assess variability within datasets, and the common coefficient of variation of several independent samples can be used to draw inferences between them. Herein, we provide estimation methods for the confidence interval for the common coefficient of variation of multiple inverse Gaussian distributions by using the generalized confidence interval (GCI), the fiducial confidence interval (FCI), the adjusted method of variance estimates recovery (MOVER), and the Bayesian credible interval (BCI) and highest posterior density (HPD) methods using the Jeffreys prior rule. The estimation methods were evaluated based on their coverage probabilities and average lengths, using a Monte Carlo simulation study. The findings indicate the superiority of the GCI over the other methods for nearly all of the scenarios considered. This was confirmed for a real-world scenario involving P M 2.5 data from three provinces in northeastern Thailand that followed inverse Gaussian distributions. [ABSTRACT FROM AUTHOR]

In this paper, we develop a discrete‐time affine option‐pricing model that explicitly incorporates the dynamics of conditional skewness. The new proposed model features different dynamics for conditional skewness and variance. To stress the difference in information, we use alternative realized measures constructed from high‐frequency historical returns to update skewness and variance dynamics. By Fourier inversion, we derive closed‐form option valuation formulas. Empirically, the flexibility that the model offers for conditional skewness as well as high‐frequency information from the underlying asset contribute to superior performance upon benchmark models using S&P 500 index options. Overall, the joint modeling of dynamic conditional skewness and realized measures leads to an out‐of‐sample gain of 12.25% in pricing accuracy. The improvements are more pronounced for deep in‐the‐money calls, options with shorter maturities, and during highly volatile periods. [ABSTRACT FROM AUTHOR]

Recently, Alizadeh and Shafaei (2023) introduced some esti- mators for the varentropy of a continuous random variable. The present article applies these estimators and constructs some tests of fit for Inverse Gaussian distribution. Percentage points and type I error of the new tests are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, a real data set is used to illustrate the application of the proposed tests [ABSTRACT FROM AUTHOR]

Accepted by: Zied Babai Exponential smoothing in state space form (ETS) is a popular forecasting technique, widely used in research and practice. While the additive error ETS models have been well studied, the multiplicative error ones have received much less attention in forecasting literature. Still, these models can be useful in cases, when one deals with positive data, because they are supposed to work in such situations. Unfortunately, the classical assumption of normality for the error term might break this property and lead to non-positive forecasts on positive data. In order to address this issue, we propose using Log-Normal, Gamma and Inverse Gaussian distributions, which are defined for positive values only. We demonstrate what happens with ETS(M,*,*) models in this case, discuss conditional moments of ETS with these distribution and show that they are more natural for the models than the Normal one. We conduct the simulation experiments in order to study the bias introduced by point forecasts in these models and then compare the models with different distributions. We finish the paper with an example of application, showing how pure multiplicative ETS with a positive distribution works. [ABSTRACT FROM AUTHOR]

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni‐modal hazard rates. In this paper, we address the problem of discriminating among these statistical distributions to consider a more appropriate lifetime model. We first consider the complete samples and make use of the maximized log‐likelihood approach for choosing the correct model. We also obtain the expressions for logarithmic of defined test statistics, and associated asymptotic distributions. We then extend our discussion based on the observed sample in the presence of some censoring. We perform a simulation study in both cases to compare the probabilities of correct selection. Furthermore, for a given probability of correct selection and user‐specified protection level, we present a discussion to determine the minimum sample size required to discriminate among the three lifetime models. Finally, two real data sets are analyzed to illustrate the proposed methodology. In our findings, we observed that model parameters and methods of estimating unknown parameters play very important roles in the discrimination process, and sample size and the proportion of censoring become key factors to ensure a high probability of selecting a correct model. [ABSTRACT FROM AUTHOR]

This study comprehensively explores the research landscape within statistical and reliability studies, focusing on the Birnbaum-Saunders distribution, Gaussian inverse distribution, cumulative damage models, and fatigue life prediction. Using a combination of bibliometric analysis, network visualization, thematic mapping, and latent Dirichlet allocation, we analyze 465 articles from the ISI Web of Science database. These articles were selected for their relevance based on a targeted search strategy. Our analysis identifies key trends, collaboration networks, and emerging research themes. Notable growth in scholarly activity was observed from 2015 to 2021, with a peak around 2021, followed by a decline in the number of publications. Relevant contributions were noted from countries such as Brazil, Canada, Chile, China, Iran, Japan, and the United States. The thematic analysis of keywords reveals influential motor themes like the Birnbaum-Saunders distribution and expectation-maximization algorithm; specialized niche areas such as producer risk; emerging or declining themes like the generalized Birnbaum-Saunders distribution; and foundational themes including cumulative damage and fatigue life distributions. A cluster analysis states key focus areas, such as material durability and advanced statistical methods. Integrating latent Dirichlet allocation, six main topics are derived, capturing broad thematic structures. However, some niche areas do not align directly due to their specialized nature and limited cross-field impact. These findings map the current research on this thematic and suggest future research directions, including deeper exploration of niche themes, integration of advanced statistical methods in practical applications, and increased collaboration across diverse research areas to enhance the robustness and applicability of reliability models. [ABSTRACT FROM AUTHOR]

The accelerated Degradation testing (ADT) experiments are important technical methods in reliability studies. Different type of accelerating degradation models has developed with the time and can be used in different types of situations. However, it has become necessary for the manager to test how many numbers of unit should be tested at a particular stress level so that the cost of testing is less. Accelerated Degradation testing (ADT) is preferred to be used in mechanized industries to obtain the required information about the reliability of product components and materials in a short period of time. Accelerated test conditions involve higher than usual pressure, temperature, voltage, vibration or any other combination of them. Data collected at such accelerated conditions are extrapolated through a physically suitable statistical model to estimate the lifetime distribution at design condition stress the life data collected from the high stresses the need to be extrapolated to estimate the life distribution under the normal-use condition. A special class of the ADT is the step-stress testing which regularly increases the stress levels at some pre-fixed time points until the test unit fails. Such experiments allow the experimenter to run the test units at higher-than-usual stress conditions in order to secure failures more quickly. The Inverse Gaussian process is flexible in incorporating random effects and explanatory variables. The different types of models based on IG process are random drift model, random volatility model and random drift-volatility model. In this paper we have considered random drift model for the study on stochastic degradation models for simple step-stress model using inverse Gaussian process observed in degradation problems. [ABSTRACT FROM AUTHOR]

The paper deals with the cost benefit analysis of a two non-identical unit cold standby system model with the implementation of preventive maintenance (PM) on the priority unit after it has operated for a random duration. The objective is to evaluate the economic viability and performance of such system. A single repairman is consistently available within the system, responsible for both PM and repair of each failed unit. The priority in repair is given to priority (p) unit over ordinary (o) unit. The failure time distribution of each unit is assumed to be exponential while the repair time distribution of both the unit is taken as inverse Gaussian. The PM time and time to PM of the priority unit are correlated having their joint distributions as bivariate exponential. By considering the regenerative point technique, various measures of system effectiveness are obtained. [ABSTRACT FROM AUTHOR]

Bayes estimation, multilayer Bayes estimation and E-Bayes estimation of inverse Gaussian distribution parameters are studied respectively under weighted p and q symmetric entropy loss, and the idea of knife cutting method is applied to Bayes estimation. The exact form of Bayes estimation of shape parameter of inverse Gaussian distribution is obtained. R software is used to numerically simulate Bayes estimation, E-Bayes estimation and Jackknife-Bayes estimation of studied parameters by using the random walk Metropolis algorithm. The Bayes estimation precision of the shape parameter of inverse Gaussian distribution under the following loss; weighted p and q symmetric entropy loss, Linex asymmetric loss, square loss and q-symmetric entropy loss is compared, and the results showed that the Bayes estimation of the shape parameter of the inverse Gaussian distribution has higher accuracy under weighted p and q symmetric entropy loss. [ABSTRACT FROM AUTHOR]

High‐breakdown‐point estimators of multivariate location and shape matrices, such as the MM‐estimator with smoothed hard rejection and the Rocke S‐estimator, are generally designed to have high efficiency for Gaussian data. However, many phenomena are non‐Gaussian, and these estimators can therefore have poor efficiency. This article proposes a new tunable S‐estimator, termed the Sq‐estimator, for the general class of symmetric elliptical distributions, a class containing many common families such as the multivariate Gaussian, t‐, Cauchy, Laplace, hyperbolic, and normal inverse Gaussian distributions. Across this class, the Sq‐estimator is shown to generally provide higher maximum efficiency than other leading high‐breakdown estimators while maintaining the maximum breakdown point. Furthermore, the Sq‐estimator is demonstrated to be distributionally robust, and its robustness to outliers is demonstrated to be on par with these leading estimators while also being more stable with respect to initial conditions. From a practical viewpoint, these properties make the Sq‐estimator broadly applicable for practitioners. These advantages are demonstrated with an example application—the minimum‐variance optimal allocation of financial portfolio investments. [ABSTRACT FROM AUTHOR]

Understanding how the adult human brain learns novel categories is an important problem in neuroscience. Drift-diffusion models are popular in such contexts for their ability to mimic the underlying neural mechanisms. One such model for gradual longitudinal learning was recently developed in Paulon et al. (J Am Stat Assoc 116:1114–1127, 2021). In practice, category response accuracies are often the only reliable measure recorded by behavioral scientists to describe human learning. Category response accuracies are, however, often the only reliable measure recorded by behavioral scientists to describe human learning. To our knowledge, however, drift-diffusion models for such scenarios have never been considered in the literature before. To address this gap, in this article, we build carefully on Paulon et al. (J Am Stat Assoc 116:1114–1127, 2021), but now with latent response times integrated out, to derive a novel biologically interpretable class of 'inverse-probit' categorical probability models for observed categories alone. However, this new marginal model presents significant identifiability and inferential challenges not encountered originally for the joint model in Paulon et al. (J Am Stat Assoc 116:1114–1127, 2021). We address these new challenges using a novel projection-based approach with a symmetry-preserving identifiability constraint that allows us to work with conjugate priors in an unconstrained space. We adapt the model for group and individual-level inference in longitudinal settings. Building again on the model's latent variable representation, we design an efficient Markov chain Monte Carlo algorithm for posterior computation. We evaluate the empirical performance of the method through simulation experiments. The practical efficacy of the method is illustrated in applications to longitudinal tone learning studies. [ABSTRACT FROM AUTHOR]

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches.

Bayesian Control charts are emerging as the most efficient statistical tools for monitoring manufacturing processes and providing effective control over process variability. The Bayesian approach is particularly suitable for addressing parametric uncertainty in the manufacturing industry. In this study, we determine the monitoring threshold for the shape parameter of the Inverse Gaussian distribution (IGD) and design different exponentially-weighted-moving-average (EWMA) control charts based on different loss functions (LFs). The impact of hyperparameters is investigated on Bayes estimates (BEs) and posterior risks (PRs). The performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MRL) are employed to evaluate the suggested approach. The designed Bayesian charts are evaluated for different settings of smoothing constant of the EWMA chart, different sample sizes, and pre-specified false alarm rates. The simulative study demonstrates the effectiveness of the suggested Bayesian method-based EWMA charts as compared to the conventional classical setup-based EWMA charts. The proposed techniques of EWMA charts are highly efficient in detecting shifts in the shape parameter and outperform their classical counterpart in detecting faults quickly. The proposed technique is also applied to real-data case studies from the aerospace manufacturing industry. The quality characteristic of interest was selected as the monthly industrial production index of aircraft from January 1980 to December 2022. The real-data-based findings also validate the conclusions based on the simulative results. [ABSTRACT FROM AUTHOR]

Sampling from matrix generalized inverse Gaussian (MGIG) distributions is required in Markov chain Monte Carlo (MCMC) algorithms for a variety of statistical models. However, an efficient sampling scheme for the MGIG distributions has not been fully developed. We here propose a novel blocked Gibbs sampler for the MGIG distributions based on the Cholesky decomposition. We show that the full conditionals of the entries of the diagonal and unit lower-triangular matrices are univariate generalized inverse Gaussian and multivariate normal distributions, respectively. Several variants of the Metropolis-Hastings algorithm can also be considered for this problem, but we mathematically prove that the average acceptance rates become extremely low in particular scenarios. We demonstrate the computational efficiency of the proposed Gibbs sampler through simulation studies and data analysis. for this article are available online. [ABSTRACT FROM AUTHOR]

The regression model is one of the important quantitative structure-activity relationship (QSAR) model tools that is used chiefly in chemometrics studies. In chemometrics, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, then the inverse Gaussian regression model (IGRM) is a better choice QSAR model. Multicollinearity in the IGRM affects the IGRM estimation and inferences. To overcome the effect of multicollinearity, biased estimators such as ridge and Liu are discussed in the literature. However, the disadvantage of using the traditional Liu estimator is that the shrinkage parameter, d, returns a negative value that severely affects the estimator's performance. To mitigate this problem, we propose a new improved Liu estimator for the IGRM. The new estimator's performance is compared with the maximum likelihood estimator (MLE) and the other biased estimators. A Monte Carlo simulation study is conducted to assess the newly proposed estimator's performance under different parametric conditions. A QSAR chemometric application is also considered to see the clear picture of the proposed estimator. The simulation and QSAR application findings demonstrate that the newly proposed estimator consistently dominates the other competitive estimators in all the evaluated conditions. [ABSTRACT FROM AUTHOR]

Using daily closing price data spreading over 3 April 1990, to 5 May 2020, this study explores the skewness and excess kurtosis behaviour across energy, metals, and agricultural commodity futures. Subsequently, it compares the fitting of an empirical distribution under normal distribution assumption with those under the Generalized Hyperbolic distribution. The generalized hyperbolic distribution includes Hyperbolic distribution, Variance-Gamma distribution, and Normal Inverse Gaussian distribution. The results show that the Normal Inverse Gaussian distribution for natural gas, gold, platinum, copper, sugar, and feeder cattle futures captures skewness as well as excess kurtosis of the daily logarithmic returns. The findings are robust to the sub-sample analysis. [ABSTRACT FROM AUTHOR]

Due to slash/burn agricultural activity and frequent forest fires, P M 2.5 has become a significant air pollution problem in Thailand, especially in the north and north east regions. Since its dispersion differs both spatially and temporally, estimating P M 2.5 concentrations discretely by area, for which the inverse Gaussian distribution is suitable, can provide valuable information. Herein, we provide derivations of the simultaneous confidence interval for the ratios of the coefficients of variation of multiple inverse Gaussian distributions using the generalized confidence interval, the Bayesian interval based on the Jeffreys' rule prior, the fiducial interval, and the method of variance estimates recovery. The efficacies of these methods were compared by considering the coverage probability and average length obtained from simulation results of daily P M 2.5 datasets. The findings indicate that in most instances, the fiducial method with the highest posterior density demonstrated a superior performance. However, in certain scenarios, the Bayesian approach using the Jeffreys' rule prior for the highest posterior density yielded favorable results. [ABSTRACT FROM AUTHOR]

In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value-at-Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing high-frequency data spanning between 1 January 2017 and 25 October 2022, with a primary focus on Bitcoin and Ethereum, our research seeks to accentuate the resilience of VaR methodology as a paramount risk assessment tool. The essence of our investigation lies in advancing the comprehension of VaR accuracy by quantitatively comparing the observed returns of both cryptocurrencies with their corresponding estimated values, with a central theme being the endorsement of the Normal Inverse Gaussian distribution as a potent model for risk measurement, particularly in the domain of high-frequency data. To bolster the statistical reliability of our results, we adopt a forward test methodology, showcasing not only a contribution to the evolution of risk assessment techniques in Finance but also underscoring the practicality of sophisticated distributional models in econometrics. Our findings not only contribute to the refinement of risk assessment methods but also highlight the applicability of such models in precisely modeling and forecasting financial risk within the dynamic realm of cryptocurrencies, epitomized by the case study of Bitcoin and Ethereum. [ABSTRACT FROM AUTHOR]

This paper uses independence-type characterizations to propose a class of test statistics which can be used for testing goodness-of-fit with several classes of null distributions. The resulting tests are consistent against fixed alternatives. Some limiting and small sample properties of the test statistics are explored. In comparison with common universal goodness-of-fit tests, the new tests exhibit better power for most of the alternatives considered, while in comparison with another characterization-based procedure, the new tests provide competitive or comparable power in various simulation settings. The handiness of the proposed tests is demonstrated through several real-data examples. [ABSTRACT FROM AUTHOR]

In this study, we propose three different test procedures by plugging the Wald (W), score (S) and likelihood ratio (LR) statistics into the computational approach test (CAT) to test the equality of inverse Gaussian means when the scale parameters are unknown and arbitrary. Restricted maximum likelihood (RML) estimators are used in developing the proposed test procedures. Since the RML estimators cannot be derived in closed-form, the bisection method is used to obtain the numerical solutions. The motivation behind using the CAT procedure is that it can easily be implemented to hypothesis testing problems without knowing the sampling distributions of the test statistics. The proposed and existing procedures are compared in terms of type I error rates and powers via an extensive Monte Carlo simulation study. In addition, a real data set is analyzed for illustration.

Introduction: Multiple myeloma (MM) is a kind of blood cancer that is caused by the malfunction of plasma cells and their uncontrolled growth, which leads to a decrease in the level of immunity and the formation of bone lesions, especially in the spine, skull, pelvis, and ribs. Common symptoms in MM patients include severe bone pain, kidney problems, anemia, and frequent infections. This study aims to employ appropriate cure models to estimate the cure fraction and prognostic factors affecting overall survival (OS) in MM patients who have undergone transplantation. Materials and Methods: This study has analyzed the medical records of 52 patients with multiple myeloma who were admitted to Taleghani Hospital affiliated with Shahid Beheshti University of Medical Sciences in Tehran from January 2010 to August 2016 and were followed up until February 2022. Four cure models were applied to the data and it determined the cure fraction in the Inverse Gaussian model is higher than in other models, so prognostic factors affecting the survival of patients were examined using this model. Results: The mean age at diagnosis was 53.07 (SD =6.4). The 5-year survival rate for MM patients was 74%, and the long-term survival rate for patients in this study was 54.7%. Using the Inverse Gaussian model, the cure fraction was estimated at 54.4% Conclusion: This study applies cure models to find prognostic factors based on pre-transplant CBC test on the survival time of MM patients who have been treated with auto-HSCT, so the number of platelets pre-transplantation and the patient's age are effective predictors for overall survival.

Compositional data (CoDa) often appear in various fields such as biology, medicine, geology, chemistry, economics, ecology and sociology. Although existing Dirichlet and related models are frequently employed in CoDa analysis, sometimes they may provide unsatisfactory performances in modelling CoDa as shown in our first real data example. First, this paper develops a multivariate compositional inverse Gaussian (CIG) model as a new tool for analysing CoDa. By incorporating the stochastic representation (SR), the expectation–maximization (EM) algorithm (aided by a one-step gradient descent algorithm) can be established to solve the parameter estimation for the proposed distribution (model). Next, zero observations may be often encountered in the real CoDa analysis. Therefore, the second aim of this paper is to propose a new model (called as ZCIG model) through a novel mixture SR based on both the CIG random vector and a so-called zero-truncated product Bernoulli random vector to model CoDa with zeros. Corresponding statistical inference methods are also developed for both cases without/with covariates. Two real data sets are analysed to illustrate the proposed statistical methods by comparing the proposed CIG and ZCIG models with existing Dirichlet and logistic-normal models. [ABSTRACT FROM AUTHOR]

The inverse Gaussian distribution, known for its flexible shape, is widely used across various applications. Existing confidence intervals for the mean parameter, such as profile likelihood, reparametrized profile likelihood, and Wald-type reparametrized profile likelihood with observed Fisher information intervals, are generally effective. However, our simulation study identifies scenarios where the coverage probability falls below the nominal confidence level. Wald-type intervals are widely used in statistics and have a symmetry property. We mathematically derive the Wald-type profile likelihood (WPL) interval and the Wald-type reparametrized profile likelihood with expected Fisher information (WRPLE) interval and compare their performance to existing methods. Our results indicate that the WRPLE interval outperforms others in terms of coverage probability, while the WPL typically yields the shortest interval. Additionally, we apply these proposed intervals to a real dataset, demonstrating their potential applicability to other datasets that follow the IG distribution. [ABSTRACT FROM AUTHOR]

The Inverse Gaussian (IG) distribution is widely used to model positively skewed data. In this article, we examine goodness of fit tests for the Inverse Gaussian distribution based on the empirical distribution function. In order to compute the test statistics, parameters of the Inverse Gaussian distribution are estimated by maximum likelihood estimators (MLEs), which are simple explicit estimators. Critical points and the actual sizes of the tests are obtained by Monte Carlo simulation. Through a simulation study, power values of the tests are compared with each other. Finally, an illustrative example is presented and analyzed. [ABSTRACT FROM AUTHOR]

The multi-dimensional vector autoregressive (VAR) time series is often used to model the impulse-response functions of macroeconomics variables. However, in some economical applications, the variable of main interest is the product of time series describing market variables, like e.g. the cost, being the product of price and volume. In this paper, we analyze the product of the bi-dimensional VAR(1) model components. For the introduced time series, we derive general formulas for the autocovariance function and study its properties for different cases of cross-dependence between the VAR(1) model components. The theoretical results are then illustrated in the simulation study for two types of bivariate distributions of the residual series, namely the Gaussian and Student's t. The obtained results are applied for the electricity market case study, in which we show that the additional cost of balancing load prediction errors prior to delivery can be well described by time series being the product of the VAR(1) model components with the bivariate normal inverse Gaussian distribution. [ABSTRACT FROM AUTHOR]

The Inverse Gaussian (IG) distribution is widely used to model positively skewed data. In this article, we examine goodness of fit tests for the Inverse Gaussian distribution based on the empirical distribution function. In order to compute the test statistics, parameters of the Inverse Gaussian distribution are estimated by maximum likelihood estimators (MLEs), which are simple explicit estimators. Critical points and the actual sizes of the tests are obtained by Monte Carlo simulation. Through a simulation study, power values of the tests are compared with each other. Finally, an illustrative example is presented and analyzed.

The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as PM2.5 levels. The coefficient of variation is often used to assess variability within datasets, and the common coefficient of variation of several independent samples can be used to draw inferences between them. Herein, we provide estimation methods for the confidence interval for the common coefficient of variation of multiple inverse Gaussian distributions by using the generalized confidence interval (GCI), the fiducial confidence interval (FCI), the adjusted method of variance estimates recovery (MOVER), and the Bayesian credible interval (BCI) and highest posterior density (HPD) methods using the Jeffreys prior rule. The estimation methods were evaluated based on their coverage probabilities and average lengths, using a Monte Carlo simulation study. The findings indicate the superiority of the GCI over the other methods for nearly all of the scenarios considered. This was confirmed for a real-world scenario involving PM2.5 data from three provinces in northeastern Thailand that followed inverse Gaussian distributions.

In the era of social media and the dominance of video-based social media sites such as TikTok, short educational movies could serve as a powerful tool for appraising environmental problems and promoting effective protection practices. According to System Theory, educational video can be observed as a complex system of various patterns of visual and acoustic codes that can be quantified and presented as Ishikawa diagrams. Through the analysis of two award-winning educational short movies on environmental protection, this paper presents the development of models for educational movie production by combining theoretical concepts of message composition from communication theory with technical enhancements based on cinemetrics, psychophysiology and statistical methods derived from the simulation modelling. Analysis of the two technical characteristics of the movies: frame (shot) length and distribution of the Red-Green-Blue colour spectrum, confirms explicated theoretical assumptions. Statistical analysis shows that technical transition points (represented by colour equilibrium and inverse Gaussian distribution of shot length) correspond to the movie narration, colour enhancements (peaks) are consistent with the elements of storytelling, and colour patterns in the movie follow psychophysiological assumptions of the meaning of colour, amplifying anticipated viewers response through unique distribution for each of the analyzed colours. Considering the acceleration of content production and the rising lack of focus of modern media consumers, the findings presented in this paper offer a useful tool for the development and production of educational and environmental video materials, its systematisation, optimisation, capacity to clarify complex environmental subjects and engage the various public. [ABSTRACT FROM AUTHOR]

Currently, Brazil is the leading producer of sugarcane in the world, with self-sufficiency in the use of ethanol as a biofuel, as well as being one of the largest suppliers of sugar to the world. This study aimed to develop a predictive model for sugarcane production based on data extracted from aerial imagery obtained from drones or satellites, allowing the precise tracking of plant development in the field. A model based on a semiparametric approach associated with the inverse Gaussian distribution applied to vegetation indices (VIs), such as the Normalized Difference Vegetation Index (NDVI) and Visible Atmospherically Resistant Index (VARI), was developed with data from drone images obtained from two field experiments with randomized replications and four sugarcane varieties. These experiments were performed under conditions identical to those applied by sugarcane farmers. Further, the model validation was carried out by scaling up the analyses with data extracted from Sentinel-2 images of several commercial sugarcane fields. Very often, in countries such as Brazil, sugarcane crops occupy extensive areas. Consequently, the development of tools capable of being operated remotely automatically benefits the management of this crop in the field by avoiding laborious and time-consuming sampling and by promoting the reduction of operation costs. The results of the model application in both sources of data, i.e., data from field experiments as well as the data from commercial fields, showed a suitable level of overlap between the data of predicted yield using VIs generated from drone and satellite images with the data of verified yield obtained by measuring the production of experiments and commercial fields, indicating that the model is reliable for forecasting productivity months before the harvest time.

The survival probability of a composite material subject to external stress is governed by the condition that the strength of the material must exceed the applied stress. There are several models proposed in the literature for studying such stress-strength relationships, especially with reference to modeling failures in carbon fiber composites. A strong contender in this group is the inverse Gaussian based cumulative damage model. The present paper outlines the Bayes analysis of the four models of this family, two for each of additive and multiplicative stress functions. Further a comparative study, based on a real data set, has been carried out to propose the best model among them. [ABSTRACT FROM AUTHOR]

Data cleaning is necessary to obtain high-quality monitoring data, which consists of two parts: anomaly identification and repair. A high-quality dataset is always used to repair data anomalies in current research, which may be difficult to obtain in practice because of the large number of data anomalies existing in real data. Besides, outliers, baseline shifts, and noise in dataset can lead to wrong missing restoration results. Therefore, the anomaly identification and location are needed to remove outliers, baseline shifts, and noise to regard the repair of these anomalies as missing data restoration. However, the identification of multiple data anomalies is time consuming and challenging. To this end, we propose a Bayesian robust tensor learning model to reconstruct the monitoring data tensor by extracting potential data features of the spatiotemporal tensor. A mixture of Laplace distribution with generalized inverse Gaussian distribution is used to model noise to enhance robustness. The tensor formed from the data containing anomalies can be input directly into the model without the identification and location of the data anomalies in advance. All data anomalies are repaired during the tensor reconstruction process. In addition, outliers, baseline shifts, and noise do not interfere with the missing restoration results owing to the robustness of the model. Furthermore, different cleaning strategies are proposed for dynamic and static response data. The data performance is verified using the real monitoring data of a concrete box girder bridge. The results show that the proposed method exhibits good data-cleaning performance when dealing with data containing a large number of data anomalies. In addition, as the abnormal rate increases, the proposed method still exhibits good data-cleaning performance. [ABSTRACT FROM AUTHOR]