One Parameter A (α) Distribution: Different Methods of Estimation

2021 ◽  
Vol 8 (1) ◽  
pp. 01-09
Author(s):  
Sanku Dey ◽  
Mahendra Saha ◽  
Sankar Goswami

This paper addresses the different methods of estimation of the unknown parameter of one parameter A(α) distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimator, least square and weighted least square estimators, maximum product spacing estimators, Cram´er-von Mises estimator and compare those using extensive numerical simulations. Next, we obtain parametric bootstrap confidence interval of the parameter using frequentist approaches. Finally, one real data set has been analysed for illustrative purposes.

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.


Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE


Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5931-5947
Author(s):  
Hatami Mojtaba ◽  
Alamatsaz Hossein

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.


2021 ◽  
Author(s):  
Lars Snipen ◽  
Inga-Leena Angell ◽  
Torbjørn Rognes ◽  
Knut Rudi

Abstract BackgroundStudies of shifts in microbial community composition has many applications. For studies at species or subspecies levels, the 16S amplicon sequencing lacks resolution, and is often replaced by full shotgun sequencing. Due to higher costs, this restricts the number of samples sequenced. As an alternative to a full shotgun sequencing we have investigated the use of Reduced Metagenome Sequencing (RMS) to estimate the composition of a microbial community. This involves the use of double-digested restriction associated DNA sequencing, which means only a smaller fraction of the genomes are sequenced. The read sets obtained by this approach have properties different from both amplicon and shotgun data, and analysis pipelines for both can either not be used at all or do not explore the full potential of RMS data.ResultsWe suggest a procedure for analyzing such data, based on fragment clustering and the use of a constrained ordinary least square de-convolution for estimating the relative abundance of all community members. Mock-community data sets shows the potential to clearly separate between strains even when the 16S is 100% identical and genome-wide differences is <0.02, indicating RMS has a very high resolution. From a simulation study we compare RMS to shotgun sequencing and show that we get improved abundance estimates when the community has many very closely related genomes. From a real data set of infants guts we show that RMS is capable of detecting a strain-diversity gradient for Escherichia coli across time.ConclusionWe find that RMS is a good alternative to either metabarcoding or shotgun sequencing when it comes to resolving microbial communities at the strain-level. Like shotgun metagenomics, it requires a good database of reference genomes, and is well suited for studies of the human gut or other communities where many reference genomes exist. A data analysis pipeline is offered, as an R package at https://github.com/larssnip/microRMS.


2021 ◽  
Vol 50 (5) ◽  
pp. 77-100
Author(s):  
Aidi khaoula ◽  
Sanku Dey ◽  
Devendra Kumar ◽  
Seddik-Ameur N

In this paper, we try to contribute to the distribution theory literature by incorporating a new bounded distribution, called the unit generalized inverse Weibull distribution (UGIWD) in the (0, 1) intervals by transformation method. The proposed distribution exhibits  increasing and bathtub shaped hazard rate function. We derive some basic statistical properties of the new distribution. Based on complete sample, the model parameters are obtained by the methods of maximum likelihood, least square, weighted least square, percentile, maximum product of spacing and Cram`er-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap confidence intervals of the parameters of the model based on aforementioned methods of estimation are also obtained. We illustrate the performance of the proposed distribution by means of one real data set and the data set shows that the new distribution is more appropriate as compared to unit Birnbaum-Saunders, unit gamma, unit Weibull, Kumaraswamy and unit Burr III distributions. Further, we construct chi-squared goodness-of-fit tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification. The criterion test used is the modified chi-squared statistic Y^2, developedby Bagdonavi?ius and Nikulin, 2011 for some parametric models when data are censored. The performances of the proposed test are shown by an intensive simulation study and an application to real data set


Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 566-571
Author(s):  
Rana A. Bakoban

AbstractThe coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.


2021 ◽  
Vol 12 (1) ◽  
pp. 76
Author(s):  
Juan A. Marin-Garcia ◽  
Angel Ruiz ◽  
Maheut Julien ◽  
Jose P. Garcia-Sabater

<p class="Abstract">This paper presents the generation of a plausible data set related to the needs of COVID-19 patients with severe or critical symptoms. Possible illness’ stages were proposed within the context of medical knowledge as of January 2021. The parameters chosen in this data set were customized to fit the population data of the Valencia region (Spain) with approximately 2.5 million inhabitants. They were based on the evolution of the pandemic between September 2020 and March 2021, a period that included two complete waves of the pandemic.</p><p class="Abstract">Contrary to expectation and despite the European and national transparency laws (BOE-A2013-12887, 2013; European Parliament and Council of the European Union, 2019), the actual COVID-19 pandemic-related data, at least in Spain, took considerable time to be updated and made available (usually a week or more). Moreover, some relevant data necessary to develop and validate hospital bed management models were not publicly accessible. This was either because these data were not collected, because public agencies failed to make them public (despite having them indexed in their databases), the data were processed within indicators and not shown as raw data, or they simply published the data in a format that was difficult to process (e.g., PDF image documents versus CSV tables). Despite the potential of hospital information systems, there were still data that were not adequately captured within these systems.</p><p class="Abstract">Moreover, the data collected in a hospital depends on the strategies and practices specific to that hospital or health system. This limits the generalization of "real" data, and it encourages working with "realistic" or plausible data that are clean of interactions with local variables or decisions (Gunal, 2012; Marin-Garcia et al., 2020). Besides, one can parameterize the model and define the data structure that would be necessary to run the model without delaying till the real data become available. Conversely, plausible data sets can be generated from publicly available information and, later, when real data become available, the accuracy of the model can be evaluated (Garcia-Sabater and Maheut, 2021).</p><p class="Abstract">This work opens lines of future research, both theoretical and practical. From a theoretical point of view, it would be interesting to develop machine learning tools that, by analyzing specific data samples in real hospitals, can identify the parameters necessary for the automatic prototyping of generators adapted to each hospital. Regarding the lines of research applied, it is evident that the formalism proposed for the generation of sound patients is not limited to patients affected by SARS-CoV-2 infection. The generation of heterogeneous patients can represent the needs of a specific population and serve as a basis for studying complex health service delivery systems.</p><p class="Abstract"> </p><p class="Abstract"> </p>


2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Rashad Bantan ◽  
Amal S. Hassan ◽  
Mahmoud Elsehetry ◽  
B. M. Golam Kibria

This paper proposed a new probability distribution, namely, the half-logistic xgamma (HLXG) distribution. Various statistical properties, such as, moments, incomplete moments, mean residual life, and stochastic ordering of the proposed distribution, are discussed. Parameter estimation of the half-logistic xgamma distribution is approached by the maximum likelihood method based on complete and censored samples. Asymptotic confidence intervals of model parameters are provided. A simulation study is conducted to illustrate the theoretical results. Moreover, the model parameters of the HLXG distribution are estimated by using the maximum likelihood, least square, maximum product spacing, percentile, and Cramer–von Mises (CVM) methods. Superiority of the new model over some existing distributions is illustrated through three real data sets.


2018 ◽  
Vol 52 (1) ◽  
pp. 43-59
Author(s):  
AMULYA KUMAR MAHTO ◽  
YOGESH MANI TRIPATH ◽  
SANKU DEY

Burr type X distribution is one of the members of the Burr family which was originally derived by Burr (1942) and can be used quite effectively in modelling strength data and also general lifetime data. In this article, we consider efficient estimation of the probability density function (PDF) and cumulative distribution function (CDF) of Burr X distribution. Eight different estimation methods namely maximum likelihood estimation, uniformly minimum variance unbiased estimation, least square estimation, weighted least square estimation, percentile estimation, maximum product estimation, Cremer-von-Mises estimation and Anderson-Darling estimation are considered. Analytic expressions for bias and mean squared error are derived. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, a real data set has been analyzed for illustrative purposes.


2020 ◽  
Author(s):  
Lars Snipen ◽  
Inga-Leena Angell ◽  
Torbjørn Rognes ◽  
Knut Rudi

Abstract Background: Studies of shifts in microbial community composition has many applications. For studies at species or subspecies levels, the 16S amplicon sequencing lacks resolution, and is often replaced by full shotgun sequencing. Due to higher costs, this restricts the number of samples sequenced. As an alternative to a full shotgun sequencing we have investigated the use of Reduced Metagenome Sequencing (RMS) to estimate the composition of a microbial community. This involves the use of double-digested restriction associated DNA sequencing, which means only a smaller fraction of the genomes are sequenced. The read sets obtained by this approach have properties different from both amplicon and shotgun data, and analysis pipelines for both can either not be used at all or do not explore the full potential of RMS data.Results: We suggest a procedure for analyzing such data, based on fragment clustering and the use of a constrained ordinary least square de-convolution for estimating the relative abundance of all community members. Mock-community data sets shows the potential to clearly separate between strains even when the 16S is 100% identical and genome-wide dierences is < 0:02, indicating RMS has a very high resolution. From a simulation study we compare RMS to shotgun sequencing and show that we get improved abundance estimates when the community has many very closely related genomes. From a real data set of infants guts we show that RMS is capable of detecting a strain-diversity gradient for Escherichia coli across time.Conclusion: We find that RMS is a good alternative to either metabarcoding or shotgun sequencing when it comes to resolving microbial communities at the strain-level. Like shotgun metagenomics, it requires a good database of reference genomes, and is well suited for studies of the human gut or other communities where many reference genomes exist. A data analysis pipeline is offered, as an R package at https://github.com/larssnip/microRMS.


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