Parameters Of Statistical Model Research Articles

Statistical image watermark decoder using high-order difference coefficients and bounded generalized Gaussian mixtures-based HMT

Imperceptibility, robustness and data payload are three main requirements of any image watermarking systems to guarantee desired functionalities, but there is a tradeoff among them from the information-theoretic perspective. In order to achieve this balance, in this paper, we propose a new statistical image watermarking scheme in nonsubsampled Shearlet transform (NSST) domain, which is based on high-order difference coefficients and bounded generalized Gaussian mixture model (BGGMM) based hidden Markov tree (HMT). In embedding process, NSST is firstly performed on host image and NSST highpass subband is divided into no-overlapping blocks. Then high-order differences of NSST coefficient blocks are computed. And finally, watermark signal is inserted into robust high-order difference coefficients through non-linear multiplicative approach. In extraction phase, robust high-order difference coefficients are firstly modeled by employing BGGMM based HMT, which can capture accurately both marginal distributions and strong dependencies of high-order difference coefficients. Statistical model parameters are then estimated by combining the approach of minimizing the higher bound on data negative log-likelihood function and upward–downward algorithm. And finally, an image watermark decoder is developed using BGGMM based HMT and maximum likelihood decision. Experimental results on some test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed scheme.

Mass-number dependence of statistical model parameters and its impact on incomplete fusion fraction calculations

Incomplete fusion processes and estimation of strength of incomplete fusion in heavy ion induced nuclear reactions have been explored for several combinations of projectile-target nuclei. Dynamics of these reactions is explained using an optical model. Parameters of the optical model affect the shape and depth of nuclear potential and hence influence the theoretical predictions. For heavy ion induced reactions, the optical model potential parameters are not unique and different sets of these parameters may be used for different ranges of mass number $A$ and incident energy $E$. To explore the effect of optical model potential parameters, a comparative study of available experimental data for excitation functions of four systems, $^{16}\mathrm{O}+^{181}\mathrm{Ta}, ^{12}\mathrm{C}+^{165}\mathrm{Ho}, ^{14}\mathrm{N}+^{163}\mathrm{Dy}$, and $^{16}\mathrm{O}+^{74}\mathrm{Ge}$, with corresponding theoretically predicted excitation functions, made by PACE4 using different sets of optical model potential parameters, has been done. It has been observed that a single set of optical model potential parameters is not adequate for all the systems. The variations in these parameters change the theoretical cross-section predictions for various channels considerably, which in turn, change the correspondingly estimated fraction of incomplete fusion $({F}_{\mathrm{ICF}})$. The effect of deformation of target nuclei on fractional incomplete fusion has also been investigated for the above mentioned systems. ${F}_{\mathrm{ICF}}$ has been plotted as a function of deformation parameter $({\ensuremath{\beta}}_{2})$ of the target nuclei and it is found to increase as the deformation parameter of the corresponding target nuclei increases on either side of the intrinsic spherical symmetry.

Wrong-way driving crash injury analysis on arterial road networks using non-parametric data mining techniques

Wrong-way driving (WWD) crashes result in more fatalities per crash, involve more vehicles, and cause extended road closures compared to other types of crashes. Previous studies have used descriptive and parametric statistical models to identify factors that affect WWD crash severity on limited access facilities. This study adopted a combination of non-parametric data mining techniques aiming to recognize the pattern of contributing factors that affect the WWD crash severity on non-limited access facilities. These non-parametric methods can handle heterogeneity in crash datasets well. In this study, hierarchical clustering was used to divide the crash dataset into homogeneous clusters. A random forests analysis was used to select important variables, and decision trees and decision rules were generated to show the underlying pattern and interactions between different factors that affect WWD crash severity. The analysis was based on 1,475 WWD crashes that occurred on arterial streets from 2012-2016 in Florida. Results show that head-on collisions, weekend days, high-speed facilities, crashes involving vehicles entering from a driveway, dark-not lighted roadways, older drivers, and driver impairment are important factors that play a crucial role in WWD crash severity on non-limited access facilities.

The Uncertainty of Confidence

This is a free-verse poem about the estimation of population parameters in statistical models. The spacing of words is intended to reflect uncertainty.

Continuous versus discrete data analysis for gait evaluation of horses with induced bilateral hindlimb lameness

BackgroundGait kinematics measured during equine gait analysis are typically evaluated by analysing (asymmetry‐based) discrete variables (eg, peak values) obtained from continuous kinematic signals (eg, timeseries of datapoints). However, when used for the assessment of complex cases of lameness, such as bilateral lameness, discrete variable analysis might overlook relevant functional adaptations.ObjectivesThe overall aim of this paper is to compare continuous and discrete data analysis techniques to evaluate kinematic gait adaptations to lameness.Study designMethod comparison.MethodsSixteen healthy Shetland ponies, enrolled in a research programme in which osteochondral defects were created on the medial trochlear ridges of both femurs, were used in this study. Kinematic data were collected at trot on a treadmill before and at 3 and 6 months after surgical intervention. Statistical parametric mapping and linear mixed models were used to compare kinematic variables between and within timepoints.ResultsBoth continuous and discrete data analyses identified changes in pelvis and forelimb kinematics. Discrete data analyses showed significant changes in hindlimb and back kinematics, where such differences were not found to be significant by continuous data analysis. In contrast, continuous data analysis provided additional information on the timing and duration of the differences found.Main limitationsA limited number of ponies were included.ConclusionsThe use of continuous data provides additional information regarding gait adaptations to bilateral lameness that is complementary to the analysis of discrete variables. The main advantage lies in the additional information regarding time dependence and duration of adaptations, which offers the opportunity to identify functional adaptations during all phases of the stride cycle, not just the events related to peak values.

Advanced Statistical Analysis of 3D Kinect Data: A Comparison of the Classification Methods

This paper focuses on the statistical analysis of mimetic muscle rehabilitation after head and neck surgery causing facial paresis in patients after head and neck surgery. Our work deals with an evaluation problem of mimetic muscle rehabilitation that is observed by a Kinect stereo-vision camera. After a specific brain surgery, patients are often affected by face palsy, and rehabilitation to renew mimetic muscle innervation takes several months. It is important to be able to observe the rehabilitation process in an objective way. The most commonly used House–Brackmann (HB) scale is based on the clinician’s subjective opinion. This paper compares different methods of supervised learning classification that should be independent of the clinician’s opinion. We compare a parametric model (based on logistic regression), non-parametric model (based on random forests), and neural networks. The classification problem that we have studied combines a limited dataset (it contains only 122 measurements of 93 patients) of complex observations (each measurement consists of a collection of time curves) with an ordinal response variable. To balance the frequencies of the considered classes in our data set, we reclassified the samples from HB4 to HB3 and HB5 to HB6—it means that only four HB grades are used for classification algorithm. The parametric statistical model was found to be the most suitable thanks to its stability, tractability, and reasonable performance in terms of both accuracy and precision.

Do Machine Learning Methods Outperform Traditional Statistical Models in Crime Prediction? A Comparison Between Logistic Regression and Neural Networks

Although machine learning (ML) methods have recently gained popularity in both academia and industry as alternative risk assessment tools for efficient decision-making, inconsistent patterns are observed in the existing literature regarding their competitiveness and utility in predicting various outcomes. Drawing on a sample of the general youth population in the U.S., we compared the predictive accuracy of logistic regression (LR) and neural networks (NNs), which are the most widely applied approaches in conventional statistics and contemporary ML methods, respectively, by adopting many theoretically relevant predictors of the future arrest outcome. Even after fully implementing rigorous ML protocols for model tuning and up-sampling and down-sampling procedures recommended in recent literature to optimize learning algorithms, NNs did not yield substantially improved performance over LR if we still rely on a conventional dataset with relatively small sample sizes and a limited number of predictors. Nonetheless, we encourage more rigorous, comprehensive, and diverse evaluation research for a complete understanding of the ML potential in predictive capacity and the contingencies in which modern ML methods can perform better than conventional parametric statistical models.

Statistical image watermarking using local RHFMs magnitudes and beta exponential distribution

The imperceptibility, robustness and data payload are widely considered as the three main properties vital for any image watermarking systems. They are complimentary to each other and hence challenging to attain the right balance between them. The statistical model-based multiplicative watermarking is an effective way to achieve the tradeoff among imperceptibility, robustness and data payload. Radial harmonic Fourier moments (RHFMs) is a strong tool in image processing, which has many advantages, such as lower noise sensitivity, powerful image description ability and geometric invariance feature. In this paper, we propose a new statistical image watermarking scheme using local RHFMs magnitudes and Beta exponential distribution model. Our image watermarking scheme consists of two parts, namely, embedding and extraction. In the embedding process, we divide the host image into no-overlapping blocks and compute the local RHFMs of image blocks, then insert the watermark signal into the robust local RHFMs magnitudes through multiplicative approach. In the extraction phase, robust local RHFMs magnitudes are firstly modeled by employing the Beta exponential distribution, where the statistical properties of local RHFMs magnitudes are captured accurately. Then the modified maximum likelihood parameter estimation (MMLE) approach is introduced to estimate the statistical parameters of Beta exponential distribution model. And finally an image watermark decoder for multiplicative watermarking is developed using Beta exponential distribution and maximum likelihood decision criterion. Experimental results on some test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed statistical image watermarking.

Dynamic foot morphology explained through 4D scanning and shape modeling

A detailed understanding of foot morphology can enable the design of more comfortable and better fitting footwear. However, foot morphology varies widely within the population, and changes dynamically as the foot is loaded during stance. This study presents a parametric statistical shape model from 4D foot scans to capture both the inter- and intra-individual variability in foot morphology. Thirty subjects walked on a treadmill while 4D scans of their right foot were taken at 90 frames-per second during stance phase. Each subject’s height, weight, foot length, foot width, arch length, and sex were also recorded. The 4D scans were all registered to a common high-quality foot scan, and a principal component analysis was done on all processed 4D scans. Elastic-net linear regression models were built to predict the principal component scores, which were then inverse transformed into 4D scans. The best performing model was selected with leave-one-out cross-validation. The chosen model predicts foot morphology across stance phase with a root-mean-square error of 5.2 ± 2.0 mm and a mean Hausdorff distance of 25.5 ± 13.4 mm. This study shows that statistical shape modeling can be used to predict dynamic changes in foot morphology across the population. The model can be used to investigate and improve foot-footwear interaction, allowing for better fitting and more comfortable footwear.

Improved inference in coupling, encoding, and decoding models and its consequence for neuroscientific interpretation

BackgroundA central goal of systems neuroscience is to understand the relationships amongst constituent units in neural populations, and their modulation by external factors, using high-dimensional and stochastic neural recordings. Parametric statistical models (e.g., coupling, encoding, and decoding models), play an instrumental role in accomplishing this goal. However, extracting conclusions from a parametric model requires that it is fit using an inference algorithm capable of selecting the correct parameters and properly estimating their values. Traditional approaches to parameter inference have been shown to suffer from failures in both selection and estimation. The recent development of algorithms that ameliorate these deficiencies raises the question of whether past work relying on such inference procedures have produced inaccurate systems neuroscience models, thereby impairing their interpretation. New methodWe used algorithms based on Union of Intersections, a statistical inference framework based on stability principles, capable of improved selection and estimation. ComparisonWe fit functional coupling, encoding, and decoding models across a battery of neural datasets using both UoI and baseline inference procedures (e.g., ℓ1-penalized GLMs), and compared the structure of their fitted parameters. ResultsAcross recording modality, brain region, and task, we found that UoI inferred models with increased sparsity, improved stability, and qualitatively different parameter distributions, while maintaining predictive performance. We obtained highly sparse functional coupling networks with substantially different community structure, more parsimonious encoding models, and decoding models that relied on fewer single-units. ConclusionsTogether, these results demonstrate that improved parameter inference, achieved via UoI, reshapes interpretation in diverse neuroscience contexts.

Categorical Stochastic Processes and Likelihood

We take a category-theoretic perspective on the relationship between probabilistic modeling and gradient based optimization. We define two extensions of function composition to stochastic process subordination: one based on a co-Kleisli category and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category of Markov kernels Stoch through a pushforward procedure.We extend stochastic processes to parametric statistical models and define a way to compose the likelihood functions of these models. We demonstrate how the maximum likelihood estimation procedure defines a family of identity-on-objects functors from categories of statistical models to the category of supervised learning algorithms Learn.Code to accompany this paper can be found on GitHub (https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood).

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering.

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.

Estimating true prevalence of Schistosoma mansoni from population summary measures based on the Kato-Katz diagnostic technique.

BackgroundThe prevalence of Schistosoma mansoni infection is usually assessed by the Kato-Katz diagnostic technique. However, Kato-Katz thick smears have low sensitivity, especially for light infections. Egg count models fitted on individual level data can adjust for the infection intensity-dependent sensitivity and estimate the ‘true’ prevalence in a population. However, application of these models is complex and there is a need for adjustments that can be done without modeling expertise. This study provides estimates of the ‘true’ S. mansoni prevalence from population summary measures of observed prevalence and infection intensity using extensive simulations parametrized with data from different settings in sub-Saharan Africa.MethodologyAn individual-level egg count model was applied to Kato-Katz data to determine the S. mansoni infection intensity-dependent sensitivity for various sampling schemes. Observations in populations with varying forces of transmission were simulated, using standard assumptions about the distribution of worms and their mating behavior. Summary measures such as the geometric mean infection, arithmetic mean infection, and the observed prevalence of the simulations were calculated, and parametric statistical models fitted to the summary measures for each sampling scheme. For validation, the simulation-based estimates are compared with an observational dataset not used to inform the simulation.Principal findingsOverall, the sensitivity of Kato-Katz in a population varies according to the mean infection intensity. Using a parametric model, which takes into account different sampling schemes varying from single Kato-Katz to triplicate slides over three days, both geometric and arithmetic mean infection intensities improve estimation of sensitivity. The relation between observed and ‘true’ prevalence is remarkably linear and triplicate slides per day on three consecutive days ensure close to perfect sensitivity.Conclusions/significanceEstimation of ‘true’ S. mansoni prevalence is improved when taking into account geometric or arithmetic mean infection intensity in a population. We supply parametric functions and corresponding estimates of their parameters to calculate the ‘true’ prevalence for sampling schemes up to 3 days with triplicate Kato-Katz thick smears per day that allow estimation of the ‘true’ prevalence.

Tropical Geometry and Machine Learning

Tropical geometry is a relatively recent field in mathematics and computer science, combining elements of algebraic geometry and polyhedral geometry. The scalar arithmetic of its analytic part preexisted in the form of max-plus and min-plus semiring arithmetic used in finite automata, nonlinear image processing, convex analysis, nonlinear control, optimization, and idempotent mathematics. Tropical geometry recently emerged in the analysis and extension of several classes of problems and systems in both classical machine learning and deep learning. Three such areas include: 1) deep neural networks with piecewise linear (PWL) activation functions; 2) probabilistic graphical models; and 3) nonlinear regression with PWL functions. In this article, we first summarize introductory ideas and objects of tropical geometry, providing a theoretical framework for both the max-plus algebra that underlies tropical geometry and its extensions to general max algebras. This unifies scalar and vector/signal operations over a class of nonlinear spaces, called weighted lattices, and allows us to provide optimal solutions for algebraic equations used in tropical geometry and generalize tropical geometric objects. Then, we survey the state of the art and recent progress in the aforementioned areas. First, we illustrate a purely geometric approach for studying the representation power of neural networks with PWL activations. Then, we review the tropical geometric analysis of parametric statistical models, such as HMMs; later, we focus on the Viterbi algorithm and related methods for weighted finite-state transducers and provide compact and elegant representations via their formal tropical modeling. Finally, we provide optimal solutions and an efficient algorithm for the convex regression problem, using concepts and tools from tropical geometry and max-plus algebra. Throughout this article, we also outline problems and future directions in machine learning that can benefit from the tropical-geometric point of view.

Spinal Muscular Atrophy after Nusinersen Therapy: Improved Physiology in Pediatric Patients with No Significant Change in Urine, Serum, and Liquor 1H-NMR Metabolomes in Comparison to an Age-Matched, Healthy Cohort.

Spinal muscular atrophy (SMA) is a genetically heterogeneous group of rare neuromuscular diseases and was until recently the most common genetic cause of death in children. The effects of 2-month nusinersen therapy on urine, serum, and liquor 1H-NMR metabolomes in SMA males and females were not explored yet, especially not in comparison to the urine 1H-NMR metabolomes of matching male and female cohorts. In this prospective, single-centered study, urine, serum, and liquor samples were collected from 25 male and female pediatric patients with SMA before and after 2 months of nusinersen therapy and urine samples from a matching healthy cohort (n = 125). Nusinersen intrathecal application was the first therapy for the treatment of SMA by the Food and Drug Administration (FDA) and the European Medicines Agency (EMA). Metabolomes were analyzed using targeted metabolomics utilizing 600 MHz 1H-NMR, parametric and nonparametric multivariate statistical analyses, machine learning, and modeling. Medical assessment before and after nusinersen therapy showed significant improvements of movement, posture, and strength according to various medical tests. No significant differences were found in metabolomes before and after nusinersen therapy in urine, serum, and liquor samples using an ensemble of statistical and machine learning approaches. In comparison to a healthy cohort, 1H-NMR metabolomes of SMA patients contained a reduced number and concentration of urine metabolites and differed significantly between males and females as well. Significantly larger data scatter was observed for SMA patients in comparison to matched healthy controls. Machine learning confirmed urinary creatinine as the most significant, distinguishing SMA patients from the healthy cohort. The positive effects of nusinersen therapy clearly preceded or took place devoid of significant rearrangements in the 1H-NMR metabolomic makeup of serum, urine, and liquor. Urine creatinine was successful at distinguishing SMA patients from the matched healthy cohort, which is a simple systemic novelty linking creatinine and SMA to the physiology of inactivity and diabetes, and it facilitates the monitoring of SMA disease in pediatric patients through non-invasive urine collection.

Using a hybrid artificial intelligence method for estimating the compressive strength of recycled aggregate self-compacting concrete

Nowadays, because of human activities, the earth's environment is in danger. So, all industries including construction and building industries should be concerned about the environment, and their activities have to be in this direction. Using waste materials in construction is one of the solutions for decreasing environmental damage, for example; using recycled aggregate in various types of concrete including self-compacting concrete (SCC). Moreover, the usage of a non-destructive method for determining the mechanical properties of concrete can improve the environmental situation. To do so, in this study the radial basis function neural network (RBFNN) assisted by firefly algorithm (FA) is proposed for predicting the compressive strength of recycled aggregate self-compacting concrete (RASCC). In these regards, the information of 310 samples of RASCC has been collected from previous studies. In this model, the water to binder ratio, age, the ratio of recycled coarse aggregate, coarse aggregate, fine aggregate, and superplasticizer have been considered as input variables, and compressive strength as the output variable. Also, an ANN model has been utilized to conduct comparisons. The performance of the models has been evaluated based on statistical parameters, and by comparing the results of the model with experimental results. The values of statistical parameters of RBFNN model (for all data: R-values:0.97 & RMSE:3.3) show that the correlation between results of the model and experimental results are high and the error of the model’s results are acceptable. Moreover, results of the models indicate that both models have good ability and acceptable accuracy for predicting the compressive strength of RASCC.

Experimental Investigation and Modeling the Compressive Behavior of NEPE Propellant under Confining Pressure

AbstractIn order to study the effects of confining pressure and strain rate on the mechanical properties of the Nitrate Ester Plasticized Polyether (NEPE) propellant, compressive tests were conducted under various confining pressure conditions and strain rates using a new‐designed active gas confining pressure testing machine. The stress‐strain curves and mechanical properties of the NEPE propellant under varying confining pressure conditions and strain rates were obtained. The results show that the compressive mechanical properties of the NEPE propellant are remarkably influenced by the confining pressure and strain rate. The compressive strength under confining pressure is obviously larger than those without applied confining pressure. With the coupled effects of the confining pressure and strain rate, the compressive strength under 5.4 MPa and 6.67×10−2 s−1 is 2.17 times of its value at room condition and 6.67×10−4 s−1. Then, based on previous tensile results, the quantified comparisons of tensile and compressive mechanical properties under different experimental conditions were presented. Finally, a nonlinear constitutive model with damage was constructed to model the effect of pressure. The statistical damage model parameters were defined as ExpDec1 function of pressure P. The calibrated model can accurately predict the mechanical behaviour of the NEPE propellant under different confining pressure conditions and strain rates.

Conception and Software Implementation of a Nuclear Data Evaluation Pipeline

We discuss the design and software implementation of a nuclear data evaluation pipeline applied for a fully reproducible evaluation of neutron-induced cross sections of 56Fe above the resolved resonance region using the nuclear model code TALYS combined with relevant experimental data. The emphasis of this paper is on the mathematical and technical aspects of the pipeline and not on the evaluation of 56Fe, which is tentative. The mathematical building blocks combined and employed in the pipeline are discussed in detail. In particular, an intuitive and unified representation of experimental data, systematic and statistical errors, model parameters and defects enables the application of the Generalized Least Squares (GLS) and its natural extension, the Levenberg-Marquardt (LM) algorithm, on a large collection of experimental data without the need for data reduction techniques as a preparatory step. The LM algorithm tailored to nuclear data evaluation takes into account the exact non-linear physics model to determine best estimates of nuclear quantities. Associated uncertainty information is derived from a second-order Taylor expansion at the maximum of the posterior distribution. We also discuss the pipeline in terms of its IT (=information technology) building blocks, such as those to efficiently manage and retrieve experimental data of the EXFOR library, which facilitates their appropriate correction, and to distribute computations on a scientific cluster. Relying on the mathematical and IT building blocks, we elaborate on the sequence of steps in the pipeline to perform the evaluation, such as the retrieval of experimental data, the correction of experimental uncertainties using marginal likelihood optimization (MLO) and after a screening of thousand TALYS parameters—including Gaussian process priors on energy dependent parameters—the fitting of about 150 parameters using the LM algorithm. The code of the pipeline including a manual and a Dockerfile for a simplified installation is available at www.nucleardata.com.

Sistem Identifikasi Tingkat Kematangan Buah Nanas Secara Non-Destruktif Berbasis Computer Vision

A computer vision-based non-destructive pineapple maturity level identification system has been realized. This research was conducted to create a system capable of identifying six indexes of pineapple maturity level. An artificial neural network is used as a classifier for the level of maturity pineapples. Artificial neural network input is a statistical parameter consisting of mean, standard deviation, variance, kurtosis, and skewness of RGB and HSV color models pineapple images. Statistical parameters of the color model with a Pearson correlation value greater than 0.5 were used to characterize pineapple images. A total of 360 pineapple images were used in the training process with a percentage of 75% of training data and 25% of validation data. An image segmentation process is applied to separate the pineapple image from the image background. The result of this research is a pineapple maturity level identification system consisting of software and hardware which is able to identify six indexes of pineapple maturity level with average accuracy value of 98,4%.

Extended Topp–Leone family of distributions as an alternative to beta and Kumaraswamy type distributions: Application to glycosaminoglycans concentration level in urine

In this paper, we introduce a modified family of distributions that unifies three different families with only one tuning parameter; the so-called exp-[Formula: see text], Topp–Leone-[Formula: see text] and exp-half-[Formula: see text] families of distributions. We study mathematical properties of the proposed family, including linear representations, quantile function, probability weighted moments, reliability parameter and stochastic ordering. One of the corresponding parametric statistical model is outlined, with estimation of the parameters by the method of maximum likelihood and investigation for possible applications to glycosaminoglycans concentration level in urine over the beta Weibull and Kumaraswamy Weibull distributions. The goodness-of-fit of five other members of the family is also assessed. Regression model is also discussed using the proposed distribution and applied to establish the relationship between the glycosaminoglycans concentration level and age of the children.