Exponential Power Distribution Research Articles

Disparities with global standards about growth references of mid-upper arm circumference-for-age for Pakistani children aged 6-60 months.

Growth reference values about mid-upper arm circumference (MUAC) are vital for assessing children's nutritional status. However, Pakistan lacks these reference values and growth charts. This study aims to develop these for children aged 6-60 months and compare them with global standards. The data were acquired from the 2018 National Nutrition Survey of Pakistan, which was conducted by the United Nations Children's Fund (UNICEF) during 2018-2019. The final study cohort comprised 57 285 children, with 51% being boys. Percentile values and charts for MUAC-for-age were developed using generalised additive models for location, scale and shape with the Box-Cox power exponential distribution. The mean MUAC was 14.21 cm (±2.07 cm) and 14.13 cm (±2.12 cm) for the boys and girls, respectively. At 60 months of age, the P3 and P97 percentiles for girls were slightly higher than those for boys. The median percentiles of Pakistani children were smaller than the World Health Organisation 2007 standards and with international references. We observed disparities in MUAC-for-age growth references among Pakistani children compared to global standards, highlighting regional, age and gender variations. This underscores the need for developing countries like Pakistan to establish their growth references.

Future Prediction for Tax Complaints to Turkish Ombudsman by Models from Polynomial Regression and Parametric Distribution

The aim of this study is to forecast the amount of tax complaints filed with the Turkish Ombudsman in the future and whether or not policymakers require a specific tax Ombudsman. The polynomial regression for discrete data set is proposed to fit the number of events of tax complaints in the period from years $2013$ to $2021$. The artificial data set is generated by models which are polynomial regression and parametric distribution. The location, scale and shape parameters are determined according to the smallest value between the observed and predicted dependent variable. After determining the smallest value for the tried values of shape parameter and the parameters of polynomial regression, the best value determined by grid search for shape parameter is around $1.07$. Thus, the heavy-tailed from of exponential power distribution is gained. The artificial data sets are generated and sorted from the smallest to biggest ones. The maximum values are around $700$ and $800$ which can be regarded as future prediction because the distance among observations is taken into account by models from polynomial regression and parametric distribution. Since the polynomial regression and the parametric models are used simultaneously for modelling, the distance among observations can also be modelled by parametric model as an alternative approach provided.

An alternative multivariate exponential power distribution

In the existing multivariate Exponential Power Distribution (EPD), the shape parameter has the tendency to affect the variability in the data leading to distorted features of the distribution. This study resolves this problem by obtaining a generalized expression in place of the constant coefficient (0.5) of the quadratic form of the multivariate EPD as a function of the shape parameter, such that the variance-covariance matrix of the data is exactly equal to the scale parameter. The density function thus obtained is a more generalized multivariate EPD that provides flexibility in depicting the true underlying characteristics of the distribution for all sample sizes.

Bayesian composite $$L^p$$-quantile regression

Abstract$$L^p$$ L p -quantiles are a class of generalized quantiles defined as minimizers of an asymmetric power function. They include both quantiles, $$p=1$$ p = 1 , and expectiles, $$p=2$$ p = 2 , as special cases. This paper studies composite $$L^p$$ L p -quantile regression, simultaneously extending single $$L^p$$ L p -quantile regression and composite quantile regression. A Bayesian approach is considered, where a novel parameterization of the skewed exponential power distribution is utilized. Further, a Laplace prior on the regression coefficients allows for variable selection. Through a Monte Carlo study and applications to empirical data, the proposed method is shown to outperform Bayesian composite quantile regression in most aspects.

Statistical inference of a step-stress model with competing risks under time censoring for alpha power exponential distribution

Accelerated life testing in a reliability experiment allows test units to be under more stress than normal (expected). Step-stress tests are a subset of accelerated life tests that raise the stress levels at specific predetermined time periods to gather data on lifetime parameters more quickly than they would under normal operating settings. Additionally, there are frequently a number of risk factors connected to the root cause of a test unit failure (mechanical, electrical, etc.). In this article, we discuss the statistical inference of a step-stress model in the presence of time censoring assuming independent alpha power exponential distribution. The point estimates of the unknown scale and shape parameters of the various causes are determined using the maximum likelihood technique under the assumption of cumulative damage. We also go through creating confidence intervals for the parameters using asymptotic distributions and the parametric bootstrap approach. Extensive Monte Carlo simulations are used to evaluate the accuracy of the estimates and the performance of the confidence intervals, and finally, an example is used to explain the methods of inference presented here.

Reliability Analysis and Its Applications for a Newly Improved Type-II Adaptive Progressive Alpha Power Exponential Censored Sample

Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context of improved adaptive progressive Type-II censored data. The parameters, reliability, and hazard functions were estimated from both classical and Bayesian viewpoints using this censoring plan. To begin, we applied the maximum likelihood estimation approach to obtain parameter, reliability, and hazard function estimators. Following that, the approximate confidence intervals for the aforementioned metrics were derived, assuming the asymptotic normality traits of the maximum likelihood estimators. Additionally, by employing the Bayesian method via the Markov chain Monte Carlo technique, the point estimators and highest posterior density intervals of various parameters were created based on the symmetric squared error loss. A simulation study that incorporates numerous scenarios was used to assess the effectiveness of various estimation methodologies. The optimal progressive censorship plans are then discussed based on a set of criteria. Finally, three applications from the engineering and medical domains have been offered as examples.

A new extension of linear failure rate distribution with estimation, simulation, and applications

In this article, we provide a new three-parameter model derived from the newly reduced Cauchy power-G family and linked to the linear failure rate model. The truncated Cauchy power linear failure rate (TCPLFR) is the name given to this distribution. The TCPLFR distribution also contains the truncated Cauchy power Rayleigh distribution and the truncated Cauchy power exponential distribution as sub-models. The TCPLFR distribution has rising, falling, and U-shaped hazard rate functions. The distribution characteristics of the TCPLFR are presented. To compute the population parameters’ point and estimated confidence intervals, the maximum likelihood approach is employed. We explore the behavior of the maximum likelihood estimates as well as the estimated confidence intervals for the model parameters using Monte Carlo simulation. To demonstrate the significance and flexibility of the TCPLFR distribution, the Akaike information criterion (D1), Bayesian information criterion (D2), consistent Akaike information criterion (D3), Hannan–Quinn information criterion (D4), and Kolmogorov–Smirnov (D5) statistic with its p-value (D6) were employed. According to a real-world data analysis, the truncated Cauchy power linear failure rate distribution outperforms alternative models with two, three, and four parameters.

Development of grid-like structure hybridised advanced sheet moulding compound composite part with characterisation and prediction of the flexural stiffness

To increase the mechanical properties of sheet moulding compound (SMC) and extend the application on structural components, cost-effective towpreg-based grid-like structures with varying spacing, layers and layout were constructed, numerically studied on the tray-based 3D part and finally defined, which were co-moulded with SMC in the one-shot compression process. The hybridisation effect on the global and local elastic flexural property was experimentally characterised for the 3D part and 2D plate. For the 2D plate, an adapted analytical model was proposed treating the hybrid SMC as a laminate of different plies. A parametric study evaluated the influence of manufacturing process variables on predictive accuracy. Plateau-shaped out-of-plane waviness in towpreg was identified as the critical variable, and one adapted exponential power distribution was tailored to capture the waviness and integrated into the analytical model. Furthermore, demand for thinner towpreg was identified.

New Lomax-G family of distributions: Statistical properties and applications

This research article introduces a new family of distributions developed using the innovative beta-generated transformation technique. Among these distributions, the focus is on the inverse exponential power distribution, which exhibits unique reverse-J, inverted bathtub, or monotonically increasing hazard functions. This paper thoroughly investigates the distribution’s key characteristics and utilizes the maximum likelihood estimation method to determine its associated parameters. To assess the accuracy of the estimation procedure, the researchers conducted a simulation experiment, revealing diminishing biases and mean square errors with increasing sample sizes, even when working with small samples. Moreover, the practical applicability of the proposed distribution is demonstrated by analyzing real-world COVID-19 and medical datasets. The article establishes that the proposed model outperforms existing models by using model selection criteria and conducting goodness-of-fit test statistics. The potential applications of this research extend to various fields where modeling and analyzing hazard functions or survival data are crucial. Additionally, the study contributes to advancing probability theory and statistical inferences.

Kalman Filter Method for Handling Missing Values in Soil Moisture Sensor Data

Several imputation techniques have been developed specifically to deal with missing values. This research used data from soil moisture sensors for 34 days where there are missing values. Size of soil moisture sensor data to be quite large. So that with the missing value, it is difficult to determine how well the imputation technique is applied. Therefore, imputation technique is performed on the generated data based on the distribution of soil moisture sensor data so that an evaluation of the utilization of the imputation technique can be carried out on large data containing missing values. The method used in this study is Kalman Filter. Evaluation using the Mean Average Percentage Error (MAPE) after intentionally removed using the Missing Completely at Random (MCAR) technique with a missing rate of 5%, 10%, and 15%. The results showed that soil moisture data has a Box-Cox power exponential distribution. It was found that for generating data, Kalman Filter method has not much different MAPE value for 100 and 1000 data with missing rate was 5%, 10%, and 15%. The results of estimating missing values with the Kalman Filter on the soil moisture sensor data are in line with the soil moisture sensor data

Quantile regression based on the skewed exponential power distribution

Bayesian quantile regression generally relies on the asymmetric Laplace distribution (ALD) as the error distribution. We consider methods for Lp -quantile regression based on the skewed exponential power distribution (SEPD). Both Bayesian and frequentist estimation procedures are outlined and compared with previous work based on the SEPD. We find that our proposed methods greatly outperform a previous method in terms of quantile estimation. Further, compared with standard quantile regression, we find that our proposed methods generally perform better in terms of root mean square error (RMSE). Empirical evidence of the statistical properties of the proposed models is provided through a simulation study. Further, a real data application illustrates their performance.

Generation of percentile curves for strength and functional abilities for boys with Duchenne muscular dystrophy.

Considering the heterogeneity of the clinical manifestations of Duchenne muscular dystrophy (DMD), it is important to describe their various clinical profiles. Thus, in this study we aimed to develop percentile curves for DMD using a battery of measures to define the patterns of functional abilities, timed tests, muscle strength, and range of motion (ROM). This retrospective data analysis was based on the records of patients with DMD using the Motor Function Measure (MFM) scale, isometric muscle strength (IS), dorsiflexion ROM, 10-meter walk test (10 MWT), and 6-minute walk test (6 MWT). Percentile curves (25th, 50th, and 75th percentiles) with MFM, IS, ROM, 10 MWT, and 6 MWT on the y axis and patient age on the x axis were constructed using the generalized additive model for location, scale, and shape, with Box-Cox power exponential distribution. There were records of 329 assessments of patients between 4 and 18 years of age. The MFM percentiles showed a gradual reduction in all dimensions. Muscle strength and ROM percentiles showed that the knee extensors were the most affected from 4 years of age, and dorsiflexion ROM negative values were noted from the age of 8 years. The 10 MWT showed a gradual increase in performance time with age. For the 6 MWT, the distance curve remained stable until 8 years, with a subsequent progressive decline. In this study we generated percentile curves that can help health professionals and caregivers follow the trajectory of disease progression in DMD patients.

Field Measurements of Wind Microclimate at the Vehicle Level on a Bridge Deck under Typical Canyon Terrain

The wind field characteristics of a bridge site are the key issues for driving the safety assessment condition of mountain canyon terrain. Field measurements on a bridge deck were conducted to investigate the microclimate wind environment at the vehicle level. The measurement points were arranged in the midspan and bridge tower regions along the bridge at vehicle height above the bridge deck. The height-dependent characteristics of the microclimate wind environment at the midspan and bridge tower regions were extensively analyzed. The results show that the mean wind profiles at midspan approximately confirm the power exponential distribution. However, the mean wind profiles show non-power-exponential distribution at the tower regions. The vertical mean wind speed profiles at the midspan and bridge tower regions were then statistically fitted and suggested. The wind speed distribution at the bridge tower regions showed obvious shielding or acceleration effects. Therefore, a typical wind envelope curve across the tower region was proposed along the driving direction. For the turbulence characteristics, turbulence intensities at the tower regions are larger than those at the midspan, and integral scales at the tower regions are smaller than those at the midspan. In this study, a double logarithm third polynomial was recommended to depict the energy distribution of the turbulence microclimate wind in the frequency domain instead of the commonly used empirical spectrum functions. Gust wind speeds were also discussed, and showed that gust wind speeds are more reasonable for evaluating vehicle driving safety and comfort in long-span bridges, especially at the tower regions.

New Insights on the Multivariate Skew Exponential Power Distribution

ABSTRACT The multivariate exponential power is a useful distribution for modeling departures from normality in data by means of a tail weight scalar parameter that regulates the non-normality of the model. The incorporation of a shape asymmetry vector into the model serves to account for potential asymmetries and gives rise to the multivariate skew exponential power distribution. This work is aimed at revisiting the skew exponential power distribution taking as a starting point its formulation as a scale mixture of skew-normal distributions. The paper provides some highlights and theoretical insights on the role played by its parameters to assess two complementary aspects of the multivariate non-normality such as directional asymmetry and tail weight behavior regardless of the asymmetry. The intuition behind both issues relies on well-known mathematical ideas about skewness maximization and convex transform stochastic orderings.

Estimation of $Pr(X<Y)$ for exponential power records

In this study, we tackle the problem of estimation of stress-strength reliability $R = P r(X < Y )$ based on upper record values for exponential power distribution. We use the maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used to compute the Bayes estimation of R since the Bayes estimator can not be obtained analytically. We also derive asymptotic confidence interval based on the asymptotic distribution of the maximum likelihood estimator of R. We consider a Monte Carlo simulation study in order to compare the performances of the maximum likelihood estimators and Bayes estimators according to mean square error criteria. Finally, a real data application is presented.

A new heavy tailed distribution with actuarial measures

Actuaries are constantly on the lookout for heavy-tailed (HT) distributions in order to model data important to business and actuarial risk problems. In this article, we describe a novel type of heavy-tailed distribution that may be used to model data in the financial disciplines. Our proposed model, identified as a Kavya-Manoharan power Lomax (KMPLo) distribution, is thoroughly studied. Some fundamental characterizations, such as the quantile function and moments, have been developed. The maximum likelihood (ML) and Bayesian (B) analytical techniques are used to acquire estimates of the unknown parameters of the new model. A detailed simulation study is undertaken to evaluate the performance of the ML and B estimators. The KMPLo model's utility is demonstrated by an application to a HT insurance loss data set. The experimental results reveal that the suggested model is more adaptable and affordable than the other seven competing models including (i) the four-parameter model is the power Lomax (PLo) model; (ii) the four-parameter models odd log-logistic modified Weibull (OLLMW), Kumaraswamy Weibull (KW), generalized modified Weibull (GMW), extended odd Weibull Lomax (EOWL), Weibull-Lomax (WL), Marshall–Olkin power Lomax (MOPLo), Marshall–Olkin alpha power Lomax (MOAPLo) and exponentiated generalized alpha power exponential (EGAPEx) distributions (iii) the five-parameter distributions; , Kumaraswamy generalized power Lomax (KGPLo) and Marshall-Olkin alpha power exponentiated Weibull (MOAPEW) distribution. In addition, certain essential actuarial metrics, such like value at risk and conditional value at risk, are determined.

Elliptical Capital Asset Pricing Models: Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale

The capital asset pricing model (CAPM) is often based on the Gaussianity or normality assumption. However, such an assumption is frequently violated in practical situations. In this paper, we introduce the symmetric CAPM considering distributions with lighter or heavier tails than the normal distribution. These distributions are symmetric and belong to the family of elliptical distributions. We pay special attention to the family members related to the normal, power-exponential, and Student-t cases, with the power-exponential distribution being particularly considered, as it has not been explored widely. Based on these cases, the expectation-maximization algorithm can be used to facilitate the estimation of model parameters utilizing the maximum likelihood method. In addition, we derive the leverage and local influence methods to carry out diagnostics in the symmetric CAPM. We conduct a detailed case study to apply the obtained results estimating the systematic risk of the financial assets of a Chilean company with real data. We employ the Akaike information criterion to conclude that the studied models provide better results than the CAPM under Gaussianity.

Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions

Families of mixtures of multivariate power exponential (MPE) distributions have already been introduced and shown to be competitive for cluster analysis in comparison to other mixtures of elliptical distributions, including mixtures of Gaussian distributions. A family of mixtures of multivariate skewed power exponential distributions is proposed that combines the flexibility of the MPE distribution with the ability to model skewness. These mixtures are more robust to variations from normality and can account for skewness, varying tail weight, and peakedness of data. A generalized expectation-maximization approach, which combines minorization-maximization and optimization based on accelerated line search algorithms on the Stiefel manifold, is used for parameter estimation. These mixtures are implemented both in the unsupervised and semi-supervised classification frameworks. Both simulated and real data are used for illustration and comparison to other mixture families.

A Mixture Autoregressive Model Based on an Asymmetric Exponential Power Distribution

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods.

Parameters and Reliability Estimation of Alpha Power Exponential Distribution under Type-II Progressive Hybrid Censoring with Applications of Engineering and Management Fields

Parameters and Reliability Estimation of Alpha Power Exponential Distribution under Type-II Progressive Hybrid Censoring with Applications of Engineering and Management Fields