On Statistical Development of Neutrosophic Gamma Distribution with Applications to Complex Data Analysis

In the absence of a correct distribution theory for complex data, neutrosophic algebra can be very useful in quantifying uncertainty. In applied data analysis, implementation of existing gamma distribution becomes inadequate for some applications when dealing with an imprecise, uncertain, or vague dataset. Most existing works have explored distributional properties of the gamma distribution under the assumption that data do not have any kind of indeterminacy. Yet, analytical properties of the gamma model for the more realistic setting when data involved uncertainties remain largely underdeveloped. This paper fills such a gap and develops the notion of neutrosophic gamma distribution (NGD). The proposed distribution represents a generalized structure of the existing gamma distribution. The basic distributional properties, including moments, shape coefficients, and moment generating function (MGF), are established. Several examples are considered to emphasize the relevance of the proposed NGD for dealing with circumstances with inadequate or ambiguous knowledge about the distributional characteristics. The estimation framework for treating vague parameters of the NGD is developed. The Monte Carlo simulation is implemented to examine the performance of the proposed model. The proposed model is applied to a real dataset for the purpose of dealing with inaccurate and vague statistical data. Results show that the NGD has better flexibility in handling real data over the conventional gamma distribution.

UROCHLOA GRASS GROWTH AS A FUNCTION OF NITROGEN AND PHOSPHORUS FERTILIZATION

The urochloa grass (Urochloa mosambicensis) is a perennial grass, C4 plant, with a high photosynthetic rate and CO2 fixation, persistent to water deficit, adapted to a wide diversity of soils and hot climate regions. Thus, the objective was to evaluate the urochloa grass growth and define the best models to estimate plant height as a function of nitrogen and phosphate fertilization. The experimental design was completely randomized, in the 2 x 2 factorial design (presence and absence of nitrogen presence and absence of phosphorus), with four replications. Was used a dose of nitrogen and phosphorus equivalent to 100 kg.ha-1 of N and 150 kg.ha-1 of P2O5, respectively. The following models were used: linear, power, gamma andlogistic to estimate plant height as a function of the following explanatory variables: days after planting, nitrogen and phosphorus doses. The criteria used to determine the best model(s) were as follows: higher adjusted coefficient of determination, lower Akaike information criterion, lower sum of square of residuals and high Willmott index. The plant height in the absence of nitrogen and phosphorus and when applied 100 kg.ha-1 of N and 150 kg.ha-1 of P2O5 was estimated more accurately by the Gamma model with high power of explanation. The adoption of the Gamma model allows to estimate the U. mosambicensis plant height, in a non-destructive manner, with high precision, speed and low cost, depending of age plant and nitrogen and phosphate fertilization.

Is eliciting dependency worth the effort? A study for the multivariate Poisson-Gamma probability model

We examine whether it is worthwhile eliciting subjective judgements to account for dependency in a multivariate Poisson-Gamma probability model. The challenge of estimating reliability during product design motivated the choice of model class. For the multivariate Poisson-Gamma model we adopt an empirical Bayes methodology to present an estimator with improved accuracy. A simulation study investigates the estimation error of this estimator for different degrees of dependency and examines the impact of dependency being mis-specified when assessed by subjective judgement. Our theoretical and simulation findings give analysts insights about the value of eliciting dependency.

A Bayesian-Deep Learning Model for Estimating COVID-19 Evolution in Spain

This work proposes a semi-parametric approach to estimate the evolution of COVID-19 (SARS-CoV-2) in Spain. Considering the sequences of 14-day cumulative incidence of all Spanish regions, it combines modern Deep Learning (DL) techniques for analyzing sequences with the usual Bayesian Poisson-Gamma model for counts. The DL model provides a suitable description of the observed time series of counts, but it cannot give a reliable uncertainty quantification. The role of expert elicitation of the expected number of counts and its reliability is DL predictions’ role in the proposed modelling approach. Finally, the posterior predictive distribution of counts is obtained in a standard Bayesian analysis using the well known Poisson-Gamma model. The model allows to predict the future evolution of the sequences on all regions or estimates the consequences of eventual scenarios.

Explosions of Cylindrical Pressure Vessels Subjected to Fire: Probabilistic Prediction of a Number of Fragments

The aim of this study was to propose a procedure for a prediction of the number of fragments generated by fire induced explosions of cylindrical pressure vessels. The prediction is carried out in terms of probabilities of individual fragment numbers. The prevailing numbers of two to four fragments are considered. The fragment number probabilities are estimated by applying data on vessel fragmentations acquired in investigations of past explosion accidents. The pressure vessel explosions known as BLEVEs are considered. The Bayesian analysis is used for the estimation of the fragment number probabilities. This analysis is carried out on the basis of Poisson-gamma model. An approach to developing a gamma prior distribution for the average number of fragments per explosion accident is proposed. The assessment of the fragment number probabilities is carried out by propagating uncertainty related to the average number of fragments to uncertainty in the fragment number probabilities. The stochastic (Monte Carlo) simulation is used for this propagation. Findings of this study are viewed as a possibility to improve the assessment of risk posed by pressure vessel explosions.

Three-dimensional study of the orbit-related structures according to sex, age and skeletal deformities

Objective: This study aimed to evaluate the relations between orbit-related structures and sex, age and skeletal deformities using cone-beam computed tomography (CBCT). Methods: This retrospective study evaluated 216 consecutive CBCT scans of patients, who were divided according to: sex (male, n=105; female, n=111), age (A1: 18-32 years, n=71; A2: 33-47 years, n=78; A3: 48-62 years, n=67), and skeletal deformities (Class I, n=70; Class II, n=75; Class III, n=71). The supraorbital foramen (SOF) location, volume of orbit, optic canal (OC) and infraorbital canal (IOC) were evaluated. Results were analyzed using the Gamma model test. The Tukey-Kramer post-hoc test was used to compare the variables with three factors (p<0.05). Results: The IOC volume showed higher values for male, A3 and class I patients. The SOF location and the orbital volume also showed higher values for male patients. Regarding the volume of CO, it showed higher values ​​for male and class I patients. Conclusions: According to our results, sex has been shown to have a significant influence on orbit-related structures. Age and skeletal deformities also influenced the volume of IOC and OC. These results eventually help the clinical practice, being useful for orbital reconstruction surgeries, anthropological studies, gender identification and identification of susceptibility to pathological conditions related to sexual dimorphism.

A New Double Truncated Generalized Gamma Model with Some Applications

The generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Indeed, we know that, from the above, it is unbounded. Data have a bounded service area in a variety of applications. A new five-parameter bounded generalized Gamma model, the bounded Weibull model with four parameters, the bounded Gamma model with four parameters, the bounded generalized Gaussian model with three parameters, the bounded exponential model with three parameters, and the bounded Rayleigh model with two parameters, is presented in this paper as a special case. This approach to the problem, which utilizes a bounded support area, allows for a great deal of versatility in fitting various shapes of observed data. Numerous properties of the proposed distribution have been deduced, including explicit expressions for the moments, quantiles, mode, moment generating function, mean variance, mean residual lifespan, and entropies, skewness, kurtosis, hazard function, survival function, r th order statistic, and median distributions. The delivery has hazard frequencies that are monotonically increasing or declining, bathtub-shaped, or upside-down bathtub-shaped. We use the Newton Raphson approach to approximate model parameters that increase the log-likelihood function and some of the parameters have a closed iterative structure. Six actual data sets and six simulated data sets were tested to demonstrate how the proposed model works in reality. We illustrate why the Model is more stable and less affected by sample size. Additionally, the suggested model for wavelet histogram fitting of images and sounds is very accurate.