On the Genesis of the Marshall-Olkin Family of Distributions via the T-X Family Approach: Statistical Modeling

In the last couple of years,there Has been an increased interest among the statisticians to dene new families of distributions by adding one or more additional parameter(s)to the baseline distribution.In this regard,a number of families have been introduced and studied.One such example is the Marshall-Olkin family of distributions that is one of the most prominent approaches used to generalize the existing distributions.Whenever,we see a new method,the natural questions come in to mind are(i)what are the genesis of the newly proposed method and(ii)how did the proposed method is obtained.No doubt,the Marshall-Olkin family is a very useful method and has attracted the researchers.But,unfortunately,the authors failed to provide the explanation about the genesis of the method that how this family of distributions is obtained.To address this issue,in this article,an attempt Has been made to provide a straight forward computation about the genesis of the Marshall-Olkin family that somehow completes its derivation.The genesis of the Marshall-Olkin family is based on the T-X family approach.Furthermore,we have showed that other extensions of the Marshall-Olkin family can also be obtained via the T-X family method.Finally,a real-life application form insurance science is presented to illustrate the newly proposed extension of the Marshall-Olkin family.

Mathematical and statistical modeling of morphometric and planar parameters of barchans in Pashoeyeh Erg in the west of Lut Desert,Iran

Barchan dunes are among the most common accumulative phenomena made by wind erosion,which are usually formed in regions where the prevailing wind direction is almost constant throughout the year and there is not enough sand to completely cover the land surface.Barchans are among the most common windy landscapes in Pashoueyeh Erg in the west of Lut Desert,Iran.This study aims to elaborate on morphological properties of barchans in this region using mathematical and statistical models.The results of these methods are very important in investigating barchan shapes and identifying their behavior.Barchan shapes were mathematically modeled by simulating them in the coordinate system through nonlinear parabolic equations,so that two separate equations were calculated for barchan windward and slip-face parabolas.The type and intensity of relationships between barchan morphology and mathematical parameters were determined by the statistical modeling.The results indicated that the existing relationships followed the power correlation with the maximum coefficient of determination and minimum error of estimate.Combining the above two methods is a powerful basis for stimulating barchans in virtual and laboratory environments.The most important result of this study is to convert the mathematical and statistical models of barchan morphology to each other.Focal length is one of the most important parameters of barchan parabolas,suggesting different states of barchans in comparison with each other.As the barchan's focal length decreases,its opening becomes narrower,and the divergence of the barchan's horns reduces.Barchans with longer focal length have greater width,dimensions,and volume.In general,identifying and estimating the morphometric and planar parameters of barchans is effective in how they move,how much they move,and how they behave in the environment.These cases play an important role in the management of desert areas.

A New Statistical Modeling Approach for Survival Analysis of Cancer Patients—Multiple Myeloma Cancer

Background: The Cox Proportional Hazard (Cox-PH) model has been a popularly used method for survival analysis of cancer data given the survival times as a function of covariates or risk factors. However, it is very seldom to see the assumptions for the application of the Cox-PH model satisfied in most of the research studies, raising questions about the effectiveness, robustness, and accuracy of the model predicting the proportion of survival times. This is because the necessary assumptions in most cases are difficult to satisfy, as well as the assessment of interaction among covariates. Methods: To further improve the therapeutic/treatment strategy for cancer diseases, we proposed a new approach to survival analysis using multiple myeloma (MM) cancer data. We first developed a data-driven nonlinear statistical model that predicts the survival times with 93% accuracy. We then performed a parametric analysis on the predicted survival times to obtain the survival function which is used in estimating the proportion of survival times. Results: The new proposed approach for survival analysis has proved to be more robust and gives better estimates of the proportion of survival than the Cox-PH model. Also, satisfying the proposed model assumptions and finding interactions among risk factors is less difficult compared to the Cox-PH model. The proposed model can predict the real values of the survival times and the identified risk factors are ranked according to the percent of contribution to the survival time. Conclusion: The new proposed nonlinear statistical model approach for survival analysis of cancer diseases is very efficient and provides an improved and innovative strategy for cancer therapeutic/treatment.

Using Statistical Modeling,Rate of Change of Pitch and Inter-Onset Interval to Distinguish Between Restful and Restless Ragas

Given that the strength of statistics lies in modelling,we are motivated to do a comparative statistical study between two types of ragas,one being aesthetically known to be restful and the other restless in nature.We first try to distinguish these two types through statistical modeling.To substantiate our findings,two more sta-tistical features are considered in the paper to separate the two categories of ragas,namely the rate of change of pitch and inter-onset interval.The experimental results are encouraging.

Statistical Model of Path Loss for Railway 5G Marshalling Yard Scenario

The railway mobile communication system is undergoing a smooth transition from the Global System for Mobile Communications-Railway(GSM-R)to the Railway 5G.In this paper,an empirical path loss model based on a large amount of measured data is established to predict the path loss in the Railway 5G marshalling yard scenario.According to the different characteristics of base station directional antennas,the antenna gain is verified.Then we propose the position of the breakpoint in the antenna propagation area,and based on the breakpoint segmentation,a large-scale statistical model for marshalling yards is established.

The impact of genotyping strategies and statistical models on accuracy of genomic prediction for survival in pigs

Background:Survival from birth to slaughter is an important economic trait in commercial pig productions.Increasing survival can improve both economic efficiency and animal welfare.The aim of this study is to explore the impact of genotyping strategies and statistical models on the accuracy of genomic prediction for survival in pigs during the total growing period from birth to slaughter.Results:We simulated pig populations with different direct and maternal heritabilities and used a linear mixed model,a logit model,and a probit model to predict genomic breeding values of pig survival based on data of individual survival records with binary outcomes(0,1).The results show that in the case of only alive animals having genotype data,unbiased genomic predictions can be achieved when using variances estimated from pedigreebased model.Models using genomic information achieved up to 59.2%higher accuracy of estimated breeding value compared to pedigree-based model,dependent on genotyping scenarios.The scenario of genotyping all individuals,both dead and alive individuals,obtained the highest accuracy.When an equal number of individuals(80%)were genotyped,random sample of individuals with genotypes achieved higher accuracy than only alive individuals with genotypes.The linear model,logit model and probit model achieved similar accuracy.Conclusions:Our conclusion is that genomic prediction of pig survival is feasible in the situation that only alive pigs have genotypes,but genomic information of dead individuals can increase accuracy of genomic prediction by 2.06%to 6.04%.

Women Entrepreneurship Index Prediction Model with Automated Statistical Analysis

Recently,gender equality and women’s entrepreneurship have gained considerable attention in global economic development.Prior to the design of any policy interventions to increase women’s entrepreneurship,it is significant to comprehend the factors motivating women to become entrepreneurs.The non-understanding of the factors can result in the endurance of low living stan-dards and the design of expensive and ineffectual policies.But female involve-ment in entrepreneurship becomes higher in developing economies compared to developed economies.Women Entrepreneurship Index(WEI)plays a vital role in determining the factors that enable theflourishment of high potential female entrepreneurs which enhances economic welfare and contributes to the economic and social fabric of society.Therefore,it is needed to design an automated and accurate WEI prediction model to improve women’s entrepreneurship.In this view,this article develops an automated statistical analysis enabled WEI predic-tive(ASA-WEIP)model.The proposed ASA-WEIP technique aims to effectually determine the WEI.The proposed ASA-WEIP technique encompasses a series of sub-processes such as pre-processing,WEI prediction,and parameter optimiza-tion.For the prediction of WEI,the ASA-WEIP technique makes use of the Deep Belief Network(DBN)model,and the parameter optimization process takes place using Squirrel Search Algorithm(SSA).The performance validation of the ASA-WEIP technique was executed using the benchmark dataset from the Kaggle repo-sitory.The experimental outcomes stated the better outcomes of the ASA-WEIP technique over the other existing techniques.

Sequential Gaussian simulation for geosystems modeling:A machine learning approach

Sequential Gaussian Simulation(SGSIM)as a stochastic method has been developed to avoid the smoothing effect produced in deterministic methods by generating various stochastic realizations.One of the main issues of this technique is,however,an intensive computation related to the inverse operation in solving the Kriging system,which significantly limits its application when several realizations need to be produced for uncertainty quantification.In this paper,a physics-informed machine learning(PIML)model is proposed to improve the computational efficiency of the SGSIM.To this end,only a small amount of data produced by SGSIM are used as the training dataset based on which the model can discover the spatial correlations between available data and unsampled points.To achieve this,the governing equations of the SGSIM algorithm are incorporated into our proposed network.The quality of realizations produced by the PIML model is compared for both 2D and 3D cases,visually and quantitatively.Furthermore,computational performance is evaluated on different grid sizes.Our results demonstrate that the proposed PIML model can reduce the computational time of SGSIM by several orders of magnitude while similar results can be produced in a matter of seconds.

Remote Sensing Image Retrieval Based on 3D-Local Ternary Pattern(LTP)Features and Non-subsampled Shearlet Transform(NSST)Domain Statistical Features

With the increasing popularity of high-resolution remote sensing images,the remote sensing image retrieval(RSIR)has always been a topic of major issue.A combined,global non-subsampled shearlet transform(NSST)-domain statistical features(NSSTds)and local three dimensional local ternary pattern(3D-LTP)features,is proposed for high-resolution remote sensing images.We model the NSST image coefficients of detail subbands using 2-state laplacian mixture(LM)distribution and its three parameters are estimated using Expectation-Maximization(EM)algorithm.We also calculate the statistical parameters such as subband kurtosis and skewness from detail subbands along with mean and standard deviation calculated from approximation subband,and concatenate all of them with the 2-state LM parameters to describe the global features of the image.The various properties of NSST such as multiscale,localization and flexible directional sensitivity make it a suitable choice to provide an effective approximation of an image.In order to extract the dense local features,a new 3D-LTP is proposed where dimension reduction is performed via selection of‘uniform’patterns.The 3D-LTP is calculated from spatial RGB planes of the input image.The proposed inter-channel 3D-LTP not only exploits the local texture information but the color information is captured too.Finally,a fused feature representation(NSSTds-3DLTP)is proposed using new global(NSSTds)and local(3D-LTP)features to enhance the discriminativeness of features.The retrieval performance of proposed NSSTds-3DLTP features are tested on three challenging remote sensing image datasets such as WHU-RS19,Aerial Image Dataset(AID)and PatternNet in terms of mean average precision(MAP),average normalized modified retrieval rank(ANMRR)and precision-recall(P-R)graph.The experimental results are encouraging and the NSSTds-3DLTP features leads to superior retrieval performance compared to many well known existing descriptors such as Gabor RGB,Granulometry,local binary pattern(LBP),Fisher vector(FV),vector of locally aggregated descriptors(VLAD)and median robust extended local binary pattern(MRELBP).For WHU-RS19 dataset,in terms of{MAP,ANMRR},the NSSTds-3DLTP improves upon Gabor RGB,Granulometry,LBP,FV,VLAD and MRELBP descriptors by{41.93%,20.87%},{92.30%,32.68%},{86.14%,31.97%},{18.18%,15.22%},{8.96%,19.60%}and{15.60%,13.26%},respectively.For AID,in terms of{MAP,ANMRR},the NSSTds-3DLTP improves upon Gabor RGB,Granulometry,LBP,FV,VLAD and MRELBP descriptors by{152.60%,22.06%},{226.65%,25.08%},{185.03%,23.33%},{80.06%,12.16%},{50.58%,10.49%}and{62.34%,3.24%},respectively.For PatternNet,the NSSTds-3DLTP respectively improves upon Gabor RGB,Granulometry,LBP,FV,VLAD and MRELBP descriptors by{32.79%,10.34%},{141.30%,24.72%},{17.47%,10.34%},{83.20%,19.07%},{21.56%,3.60%},and{19.30%,0.48%}in terms of{MAP,ANMRR}.The moderate dimensionality of simple NSSTds-3DLTP allows the system to run in real-time.

An Application of Machine Learning to Thalassemia Diagnosis

Mediterranean anemia is a genetic disease that currently relies heavily on expert clinical experience to determine whether patients are affected. This method is overly reliant on expert experience and is not precise enough. This paper proposes two modeling methods to predict whether patients have Mediterranean anemia. The first method involves using Principal Component Analysis (PCA) to reduce the dimensionality of the data, followed by logistic regression modeling (PCA-LR) on the reduced dataset. The second method involves building a Partial Least Squares Regression (PLS) model. Experimental results show that the prediction accuracy of the PCA-LR model is 87.5% (degree = 2, λ=4), and the prediction accuracy of the PLS model is 92.5% (ncomp = 4), indicating good predictive performance of the models.

Review of Statistical Water Temperature Models for a Peruvian Andean River

The rapid increase in Water Temperature Rivers (WTR) observed globally in recent decades and projections for the coming decades under climate change scenarios make water temperature prediction essential to assess changes in aquatic biota. Statistical models for stream temperature prediction have been widely used because they are computationally simple, involve few parameters, and because of their relatively good accuracy. However, these models have not been evaluated in Peruvian Andean rivers. This work evaluates the main water temperature statistical models from the literature and fits them with data recorded in the Ichu River experimental watershed, Huancavelica-Peru. Three well-known models were reviewed: the Stefan & Preud’homme linear regression model and the Mohseni & Stefan 3- and 4-parameter logistic regression models. Ichu river water temperatures were simulated using the SWAT (Soil and Water Assessment Tool) hydrometeorological model, which defaults to the Stefan & Preud’homme model. Modifications and adjustment of coefficients of the evaluated models were configured in the SWAT code using the “Latin Hypercube Sampling” technique. The evaluated models showed poor performance in predicting the water temperature in the Ichu River with NSE (Nash-Sutcliffe Efficiency) values ranging from -2.6 to 0.49, while the modified models showed NSE values of 0.72 in all three cases. Findings suggest that the statistical models shown in the literature should be validated for Andean rivers.

Adaptive Maneuvering Frequency Method of Current Statistical Model

Current statistical model(CSM) has a good performance in maneuvering target tracking. However, the fixed maneuvering frequency will deteriorate the tracking results, such as a serious dynamic delay, a slowly converging speedy and a limited precision when using Kalman filter(KF) algorithm. In this study, a new current statistical model and a new Kalman filter are proposed to improve the performance of maneuvering target tracking. The new model which employs innovation dominated subjection function to adaptively adjust maneuvering frequency has a better performance in step maneuvering target tracking, while a fluctuant phenomenon appears. As far as this problem is concerned, a new adaptive fading Kalman filter is proposed as well. In the new Kalman filter, the prediction values are amended in time by setting judgment and amendment rules,so that tracking precision and fluctuant phenomenon of the new current statistical model are improved. The results of simulation indicate the effectiveness of the new algorithm and the practical guiding significance.

From statistical analysis to process optimization during cladding using a Nd:YAG laser

Application of statistical methods to optimize the process parameters was achieved by employing full factorial design of experiments,which was accomplished by cladding using stepwise ramped laser power.The correlations between clad geometry and dilution(clad characteristics)and the main process parameters laser power(P_(l)),cladding speed(v_(c)),the powder feed rate(m)were obtained through application of variance analysis technique(ANOVA).The obtained correlations between the main processing parameters and the clad characteristics are discussed and a statistical model was developed.The desirability investigations using the developed statistical model were performed by considering the clad geometry,aspect ratio,dilution and hardness.Optimal parameters for cladding Stellite 6 on AISI 420 steel substrate and for cladding Nucalloy 488V on S355 J2 steel substrate were obtained.The optimal processing parameters can be applied to clad other materials with similar chemical compositions.

Using statistical models and GIS to delimit the groundwater recharge potential areas and to estimate the infiltration rate: A case study of Nadhour-Sisseb-El Alem Basin, Tunisia

The water resources of the Nadhour-Sisseb-El Alem Basin in Tunisia exhibit semi-arid and arid climatic conditions.This induces an excessive pumping of groundwater,which creates drops in water level ranging about 1-2 m/a.Indeed,these unfavorable conditions require interventions to rationalize integrated management in decision making.The aim of this study is to determine a water recharge index(WRI),delineate the potential groundwater recharge area and estimate the potential groundwater recharge rate based on the integration of statistical models resulted from remote sensing imagery,GIS digital data(e.g.,lithology,soil,runoff),measured artificial recharge data,fuzzy set theory and multi-criteria decision making(MCDM)using the analytical hierarchy process(AHP).Eight factors affecting potential groundwater recharge were determined,namely lithology,soil,slope,topography,land cover/use,runoff,drainage and lineaments.The WRI is between 1.2 and 3.1,which is classified into five classes as poor,weak,moderate,good and very good sites of potential groundwater recharge area.The very good and good classes occupied respectively 27%and 44%of the study area.The potential groundwater recharge rate was 43%of total precipitation.According to the results of the study,river beds are favorable sites for groundwater recharge.

Using a skillful statistical model to predict September sea ice covering Arctic shipping routes

The rapid decrease in Arctic sea ice cover and thickness not only has a linkage with extreme weather in the midlatitudes but also brings more opportunities for Arctic shipping routes and polar resource exploration,both of which motivate us to further understand causes of sea-ice variations and to obtain more accurate estimates of seaice cover in the future.Here,a novel data-driven method,the causal effect networks algorithm,is applied to identify the direct precursors of September sea-ice extent covering the Northern Sea Route and Transpolar Sea Route at different lead times so that statistical models can be constructed for sea-ice prediction.The whole study area was also divided into two parts:the northern region covered by multiyear ice and the southern region covered by seasonal ice.The forecast models of September sea-ice extent in the whole study area(TSIE)and southern region(SSIE)at lead times of 1–4 months can explain over 65%and 79%of the variances,respectively,but the forecast skill of sea-ice extent in the northern region(NSIE)is limited at a lead time of 1 month.At lead times of 1–4 months,local sea-ice concentration and sea-ice thickness have a larger influence on September TSIE and SSIE than other teleconnection factors.When the lead time is more than 4 months,the surface meridional wind anomaly from northern Europe in the preceding autumn or early winter is dominant for September TSIE variations but is comparable to thermodynamic factors for NSIE and SSIE.We suggest that this study provides a complementary approach for predicting regional sea ice and is helpful in evaluating and improving climate models.

A Fuzzy Adaptive Algorithm Based on“Current”Statistical Model for Maneuvering Target Tracking

The basic"current"statistical model and adaptive Kalman filter algorithm can not track a weakly maneuvering target precisely,though it has good estimate accuracy for strongly maneuvering target.In order to solve this problem,a novel nonlinear fuzzy membership function was presented to adjust the upper and lower limit of target acceleration adaptively,and then the validity of the new algorithm for feeblish maneuvering target was proved in theory.At last,the computer simulation experiments indicated that the new algorithm has a great advantage over the basic"current"statistical model and adaptive algorithm.

Forecasting S&P 500 Stock Index Using Statistical Learning Models

Forecasting the movement of stock market is a long-time attractive topic. This paper implements different statistical learning models to predict the movement of S&P 500 index. The S&P 500 index is influenced by other important financial indexes across the world such as commodity price and financial technical indicators. This paper systematically investigated four supervised learning models, including Logistic Regression, Gaussian Discriminant Analysis (GDA), Naive Bayes and Support Vector Machine (SVM) in the forecast of S&P 500 index. After several experiments of optimization in features and models, especially the SVM kernel selection and feature selection for different models, this paper concludes that a SVM model with a Radial Basis Function (RBF) kernel can achieve an accuracy rate of 62.51% for the future market trend of the S&P 500 index.

SOUND SOURCE LOCALIZATION OF DIGITAL HEARING AIDS USING WAVELET BASED MULTIVARIATE STATISTICAL METHOD

The letter proposed a sound source localization method of digital hearing aids using wavelet based multivariate statistics with the Generalized Cross Correlation (GCC) algorithm. Haar wavelet is used to decompose GCC sequences and extract four wavelet characteristics. And then, Hotelling T2 statistical method is used to fuse the four wavelet characteristics. The statistical value is used to judge the number of sound sources and obtain corresponding time delay estimation which is used to localize the position of sound source. The experimental results show that the proposed method has better robustness in an environment with severe noise and reverberation. Meanwhile, the complexity of al-gorithm is moderate, which is available for sound source localization of hearing aids.

Sensitivity of Statistical Models for Extremes Rainfall Adjustment Regarding Data Size: Case of Ivory Coast

The objective of this study is to analyze the sensitivity of the statistical models regarding the size of samples. The study carried out in Ivory Coast is based on annual maximum daily rainfall data collected from 26 stations. The methodological approach is based on the statistical modeling of maximum daily rainfall. Adjustments were made on several sample sizes and several return periods (2, 5, 10, 20, 50 and 100 years). The main results have shown that the 30 years series (1931-1960;1961-1990;1991-2020) are better adjusted by the Gumbel (26.92% - 53.85%) and Inverse Gamma (26.92% - 46.15%). Concerning the 60-years series (1931-1990;1961-2020), they are better adjusted by the Inverse Gamma (30.77%), Gamma (15.38% - 46.15%) and Gumbel (15.38% - 42.31%). The full chronicle 1931-2020 (90 years) presents a notable supremacy of 50% of Gumbel model over the Gamma (34.62%) and Gamma Inverse (15.38%) model. It is noted that the Gumbel is the most dominant model overall and more particularly in wet periods. The data for periods with normal and dry trends were better fitted by Gamma and Inverse Gamma.

A statistical mechanics model of carbon nanotube macro-films

Carbon nanotube macro-films are two-dimensional films with micrometer thickness and centimeter by centimeter in-plane dimension.These carbon nanotube macroscopic assemblies have attracted significant attention from the material and mechanics communities recently because they can be easily handled and tailored to meet specific engineering needs.This paper reports the experimental methods on the preparation and characterization of single-walled carbon nanotube macro-films,and a statistical mechanics model on the deformation behavior of this material.This model provides a capability to optimize the synthesis process by comparing with the experiments.