method of maximum likelihood
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Author(s):  
Gerald Ikechukwu Onwuka ◽  
Abraham Iorkaa Asongo ◽  
Ishako Ara Bako ◽  
Collins Aondona Ortese ◽  
Hassan Allahde

Nigeria’s effort to reduce under-five mortality has been biased in favour of childhood mortality to the neglect of neonates and as such the literature is short of adequate information on the determinants of neonatal mortality, whereas studies have shown that about half of infant deaths occur in the neonatal period. Knowledge of the determinants of neonatal mortality is essential for the design of intervention programmes that will enhance neonatal survival. Therefore, this study was conducted to investigate the trends in neonatal mortality in Nigeria. It also proposed a Poisson based continuous probability distribution called Poisson-Lindley distribution to neonatal mortality rate in Nigeria. Some properties of the new model and other relevant measures were obtained. The unknown parameters of the model were also estimated using the method of maximum likelihood. The fitness of the proposed model to the neonatal mortality rate was considered using a dataset on neonatal mortality rate from 1967 to 2019.


2021 ◽  
pp. 49-61
Author(s):  
Валерій Костянтинович Волосюк ◽  
Володимир Володимирович Павліков ◽  
Семен Сергійович Жила ◽  
Анатолій Владиславович Попов ◽  
Володимир Віталійович Кошарський ◽  
...  

Using the method of maximum likelihood, the optimal algorithm of polarization-Doppler selection of objects on the background of the underlying surface, hydrometeors, urban buildings from aerospace carriers of radio electronic equipment has been synthesized. To solve the problem polarimetric properties of the scattered electromagnetic radiation of natural environments and anthropogenic objects were analyzed.The functional-deterministic mathematical model of the useful signalis determined. When solving the optimization problem, the method of maximum likelihood functionality and likelihood functionality for correlated processes were used, which contains the inverse matrix of inverse correlation functions of the observation equation. The obtained signal processing algorithm includes operations of spectral resection of passive interference. Polarization compensation of passive interference is performed by a combination of interchannel subtraction of the reflected signals of different polarizations. The quasi-optimal features of the synthesized algorithm, which has an obvious physical value and is optimal in the absence of internal noise, are considered. Based on the obtained results, a block diagram of the polarization-Doppler noise compensator and selection of useful signals against the background of noise reflections from the earth's surface has been developed. The study of the physical characteristics of the elements of the polarization covariance matrix of interferences at a high level of correlation of reflections of passive interferences of different polarizations is conducted.Based on the obtained results, it is proposed to introduce indicators of efficiency of passive interference compensation and selection of useful signals. The results of the analysis of the obtained indicators depending on the coefficient of the ratio of variances of passive interference indicate the need to use the polarization differences between signals and interference for selecting objects against the background of the underlying surface. The results obtained can be used to create ground-based and aerospace-based radar systems for detecting moving objects and objects with pronounced polarization features.


Author(s):  
Zafar Iqbal ◽  
Muhammad Rashad ◽  
Iram Rauf ◽  
Muhammad Salman

A new BEME distribution known as beta Exponentiated moment exponential (BEME) distribution is proposed. We provide here some shape properties, moments in the form of special functions, mean deviations of BEME distribution. We derive mathematical properties of the BEME distribution including the reliability measures, the Bonferroni and the Lorenz curves, rth order statistics, measures of uncertainty: the Shannon entropy measure and the s-entropy measure. The parameters of the BEME distribution are estimated by the method of maximum likelihood estimation and estimated non-linear equations for these estimates are presented. The application of BEME distribution is explored in three different fields of engineering.


Author(s):  
Abdulzeid Yen Anafo ◽  
Lewis Brew ◽  
Suleman Nasiru

In this paper, we propose a three-parameter probability distribution called equilibrium renewal Burr XII distribution using the equilibrium renewal process. The statistical properties of the distribution such as moment, mean deviation, order statistics, moment generating function, Beforroni and Lorenz curve, survival function, reversed hazard rate and hazard function were derived. The method of maximum likelihood is used for estimating the distribution's parameters and a simulation study is conducted to assess the performance of the parameters. We provide two applications in eld of health to demonstrate the importance of the proposed distribution.


Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2477
Author(s):  
Seitebaleng Makgai ◽  
Andriette Bekker ◽  
Mohammad Arashi

The Dirichlet distribution is a well-known candidate in modeling compositional data sets. However, in the presence of outliers, the Dirichlet distribution fails to model such data sets, making other model extensions necessary. In this paper, the Kummer–Dirichlet distribution and the gamma distribution are coupled, using the beta-generating technique. This development results in the proposal of the Kummer–Dirichlet gamma distribution, which presents greater flexibility in modeling compositional data sets. Some general properties, such as the probability density functions and the moments are presented for this new candidate. The method of maximum likelihood is applied in the estimation of the parameters. The usefulness of this model is demonstrated through the application of synthetic and real data sets, where outliers are present.


2021 ◽  
Vol 16 (4) ◽  
pp. 2993-3007
Author(s):  
Nofiu Idowu Badmus ◽  
Mary Idowu Akinyemi ◽  
Josephine Nneamaka Onyeka-Ubaka

For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Wen-Qi Duan ◽  
Zahid Khan ◽  
Muhammad Gulistan ◽  
Adnan Khurshid

The exponential distribution has always been prominent in various disciplines because of its wide range of applications. In this work, a generalization of the classical exponential distribution under a neutrosophic environment is scarcely presented. The mathematical properties of the neutrosophic exponential model are described in detail. The estimation of a neutrosophic parameter by the method of maximum likelihood is discussed and illustrated with examples. The suggested neutrosophic exponential distribution (NED) model involves the interval time it takes for certain particular events to occur. Thus, the proposed model may be the most widely used statistical distribution for the reliability problems. For conceptual understanding, a wide range of applications of the NED in reliability engineering is given, which indicates the circumstances under which the distribution is suitable. Furthermore, a simulation study has been conducted to assess the performance of the estimated neutrosophic parameter. Simulated results show that imprecise data with a larger sample size efficiently estimate the unknown neutrosophic parameter. Finally, a complex dataset on remission periods of cancer patients has been analyzed to identify the importance of the proposed model for real-world case studies.


Author(s):  
Aladesuyi Alademomi ◽  
Philips Samuel Ademola ◽  
Adefolarin Adekunle David

This paper introduces a new three parameter Rayleigh distribution which generalizes the Rayleigh distribution. The new model is referred to as Extended Rayleigh (ER) distribution. Various mathematical properties of the new model including ordinary and incomplete moment, quantile function, generating function are derived. We propose the method of maximum likelihood for estimating the model parameters. A real life data set is used to compare the flexibility of the new model with other models.


The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. it has an increasing hazard rate. The Exponentiated Gumbel distribution has applications in hydrology, meteorology, climatology, insurance, finance and geology, among many others. In this paper Firstly, the mathematical and statistical characteristics of the gumbel and Exponentiated Gumbel distribution are presented, then the applications of this distributions are studied using the real data set. Its first moment about origin and moments about mean have been obtained and expressions for skewness, kurtosis have been given. Estimation of its parameter has been discussed using the method of maximum likelihood. In the end, two applications of the gumbel and exponentiated gumbel distribution have been discussed with two real lifetime data sets. The results also confirmed the suitability of the Exponentiated Gumbel distribution for real data collection.


2021 ◽  
Vol 34 (3) ◽  
pp. 670-681
Author(s):  
EFRAIM MARTINS ARAÚJO ◽  
GEORGE LEITE MAMEDE

ABSTRACT The work evaluated the potential for discrimination of land use and occupation around reservoirs, using spectral information obtained by multispectral, hyperspectral satellites and images obtained with an ARP (remotely piloted aircraft). The research analyzed the performance of different images classification techniques applied to multispectral and hyperspectral sensors for the detection and differentiation of soil classes around the Paus Brancos and Marengo reservoirs, located in Settlement 25 of Maio. The classes identified based on surveys in campaigns carried out in 2014 and 2015 around the reservoirs were: water, macrophytes, exposed soil, native vegetation, agriculture, thin and ebbing vegetation, in addition to the cloud and cloud shadow targets. The performance of the classifiers applied to the image of the Hyperion sensor was, in general, superior to those obtained in Landsat 8 image, which can be explained by the high spectral resolution of the first, which facilitates the differentiation of targets with similar spectral response. For validation of the supervised classification method of Maximum Likelihood, Landsat 8 (08/24/2015) and Hyperion (08/28/2015) images were used. The results of the application indicated a good performance of the classifier associated with the RGB composition of the chosen Hyperion image (bands R - 51, G - 161, B - 19) in the detection of the classes around this reservoir, producing a Kappa coefficient of 0.83. The availability of data from the Hyperion sensor is very restricted, which hinders the development of continued research, thus the use of images surpassed by RPA is extremely viable.


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