An Inferential Aptness of a Weibull Generated Distribution and Application

In this article an attempt has been made to develop a flexible single parameter continuous distribution using Weibull distribution. The Weibull distribution is most widely used lifetime distributions in both medical and engineering sectors. The exponential and Rayleigh distribution is particular case of Weibull distribution. Here in this study we use these two distributions for developing a new distribution. Important statistical properties of the proposed distribution is discussed such as moments, moment generating and characteristic function. Various entropy measures like Rényi, Shannon and cumulative entropy are also derived. The kthkt⁢h order statistics of pdf and cdf also obtained. The properties of hazard function and their limiting behavior is discussed. The maximum likelihood estimate of the parameter is obtained that is not in closed form, thus iteration procedure is used to obtain the estimate. Simulation study has been done for different sample size and MLE, MSE, Bias for the parameter λλ has been observed. Some real data sets are used to check the suitability of model over some other competent distributions for some data sets from medical and engineering science. In the tail area, the proposed model works better. Various model selection criterion such as -2LL, AIC, AICc, BIC, K-S and A-D test suggests that the proposed distribution perform better than other competent distributions and thus considered this as an alternative distribution. The proposed single parameter distribution is found more flexible as compare to some other two parameter complicated distributions for the data sets considered in the present study.

Exploring the Relationship between Forest Canopy Height and Canopy Density from Spaceborne LiDAR Observations

Forest structure is a useful proxy for carbon stocks, ecosystem function and species diversity, but it is not well characterised globally. However, Earth observing sensors, operating in various modes, can provide information on different components of forests enabling improved understanding of their structure and variations thereof. The Ice, Cloud and Elevation Satellite (ICESat) Geoscience Laser Altimeter System (GLAS), providing LiDAR footprints from 2003 to 2009 with close to global coverage, can be used to capture elements of forest structure. Here, we evaluate a simple allometric model that relates global forest canopy height (RH100) and canopy density measurements to explain spatial patterns of forest structural properties. The GLA14 data product (version 34) was applied across subdivisions of the World Wildlife Federation ecoregions and their statistical properties were investigated. The allometric model was found to correspond to the ICESat GLAS metrics (median mean squared error, MSE: 0.028; inter-quartile range of MSE: 0.022–0.035). The relationship between canopy height and density was found to vary across biomes, realms and ecoregions, with denser forest regions displaying a greater increase in canopy density values with canopy height, compared to sparser or temperate forests. Furthermore, the single parameter of the allometric model corresponded with the maximum canopy density and maximum height values across the globe. The combination of the single parameter of the allometric model, maximum canopy density and maximum canopy height values have potential application in frameworks that target the retrieval of above-ground biomass and can inform on both species and niche diversity, highlighting areas for conservation, and potentially enabling the characterisation of biophysical drivers of forest structure.

A new model for predicting boiling points of alkanes

A general perception among researchers is that boiling points, which is a key property in the optimization of lubricant performance, are difficult to predict successfully using a single-parameter model. In this contribution, we propose a new graph parameter which we call, for lack of better terminology, the conduction of a graph. We exploit the conduction of a graph to develop a single-parameter model for predicting the boiling point of any given alkane. The model was used to predict the boiling points for three sets of test data and predicted with a coefficient of determination, $$R^2=0.7516,~0.7898$$ R 2 = 0.7516 , 0.7898 and 0.6488, respectively. The accuracy of our model compares favourably to the accuracy of experimental data in the literature. Our results have significant implications on the estimation of boiling points of chemical compounds in the absence of experimental data.

On intermediate statistics across many-body localization transition

The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian ensemble -- a single parameter model of level statistics proposed recently in the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa distribution is also} only slightly inferior to the two-parameter $\beta$-h ansatz shown {earlier} to reproduce {level statistics of} physical systems remarkably well.

Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes.

Reliability of the Multiplex CytoBead CeliAK Immunoassay to Assess Anti-tTG IgA for Celiac Disease Screening

Background and Objective: The diagnosis of Celiac Disease (CD) is first based on the positivity for specific serological markers. The CytoBead CeliAK immunoassay simultaneously measures antibodies (IgA) directed to tissue transglutaminase (tTG), endomysium (EMA), and deamidated gliadin (DG), in addition to providing a control for total IgA levels. The aim of this study is to assess the reliability of this multiplex assay to detect anti-tTG IgA positive patients, compared with a conventional single-parameter enzyme-linked immunosorbent assay (ELISA).Methods: Serum samples from 149 pediatric patients were assessed by both CytoBead CeliAK immunoassay and ELISA, in order to evaluate their concordance for the measurement of anti-tTG IgA.Results: The measurement of anti-tTG IgA by CytoBead CeliAK immunoassay basically showed a complete concordance rate with the conventional and single-parameter ELISA, according to the respective cutoff values (3 U/ml and 10 U/ml).Conclusions: Our comparative analysis demonstrates a substantial equivalency between multiplex CytoBead CeliAK assay and the single-parameter conventional ELISA to assess anti-tTG IgA antibody in the context of the screening for CD in children. Importantly, CytoBead CeliAK assay could present some preanalytic, analytic, and economic advantages.

Optical Turbulence Profile Forecasting and Verification in the Offshore Atmospheric Boundary Layer

A backpropagation neural network (BPNN) approach is proposed for the forecasting and verification of optical turbulence profiles in the offshore atmospheric boundary layer. To better evaluate the performance of the BPNN approach, the Holloman Spring 1999 thermosonde campaigns (HMNSP99) model for outer scale, and the Hufnagel/Andrew/Phillips (HAP) model for a single parameter are selected here to estimate profiles. The results have shown that the agreement between the BPNN approach and the measurement is very close. Additionally, statistical operators are used to quantify the performance of the BPNN approach, and the statistical results also show that the BPNN approach and measured profiles are consistent. Furthermore, we focus our attention on the ability of the BPNN approach to rebuild integrated parameters, and calculations show that the BPNN approach is reliable. Therefore, the BPNN approach is reasonable and remarkable for reconstructing the strength of optical turbulence of the offshore atmospheric boundary layer.