scholarly journals A new class of skew-logistic distribution

2019 ◽  
Vol 13 (4) ◽  
pp. 375-385
Author(s):  
Saeed Mirzadeh ◽  
Anis Iranmanesh
Keyword(s):  
Exponential Family ◽  
Real Data ◽  
Statistical Characteristics ◽  
Logistic Distribution ◽  
Simulation Studies ◽  
Data Set ◽  
The Real ◽  
New Class ◽  
Skewness Parameter

Abstract In this study, the researchers introduce a new class of the logistic distribution which can be used to model the unimodal data with some skewness present. The new generalization is carried out using the basic idea of Nadarajah (Statistics 48(4):872–895, 2014), called truncated-exponential skew-logistic (TESL) distribution. The TESL distribution is a member of the exponential family; therefore, the skewness parameter can be derived easier. Meanwhile, some important statistical characteristics are presented; the real data set and simulation studies are applied to evaluate the results. Also, the TESL distribution is compared to at least five other skew-logistic distributions.

scholarly journals The Beta Weibull-G Family of Distributions: Model, Properties and Application

2018 ◽  
Vol 7 (2) ◽  
pp. 12 ◽  
Author(s):  
Boikanyo Makubate ◽  
Broderick O. Oluyede ◽  
Gofaone Motobetso ◽  
Shujiao Huang ◽  
Adeniyi F. Fagbamigbe
Keyword(s):  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Generalized Distributions ◽  
Special Cases

A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series expansion of the density function, hazard function, moments, mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates of the model parameters are given. Application of the model to real data set is presented to illustrate the importance and usefulness of the special case beta Weibull-log-logistic distribution.

scholarly journals A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 339 ◽  
Author(s):  
Mustapha Muhammad ◽  
Lixia Liu
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Real Data ◽  
Strength Parameter ◽  
Logistic Distribution ◽  
Strength Analysis ◽  
Model Parameters ◽  
Simulation Studies ◽  
Data Set ◽  
Leibler Divergence

In this paper, we introduced a new three-parameter probability model called Poisson generalized half logistic (PoiGHL). The new model possesses an increasing, decreasing, unimodal and bathtub failure rates depending on the parameters. The relationship of PoiGHL with the exponentiated Weibull Poisson (EWP), Poisson exponentiated Erlang-truncated exponential (PEETE), and Poisson generalized Gompertz (PGG) model is discussed. We also characterized the PoiGHL sub model, i.e the half logistic Poisson (HLP), based on certain functions of a random variable by truncated moments. Several mathematical and statistical properties of the PoiGHL are investigated such as moments, mean deviations, Bonferroni and Lorenz curves, order statistics, Shannon and Renyi entropy, Kullback-Leibler divergence, moments of residual life, and probability weighted moments. Estimation of the model parameters was achieved by maximum likelihood technique and assessed by simulation studies. The stress-strength analysis was discussed in detail based on maximum likelihood estimation (MLE), we derived the asymptotic confidence interval of R = P ( X 1 < X 2 ) based on the MLEs, and examine by simulation studies. In three applications to real data set PoiGHL provided better fit and outperform some other popular distributions. In the stress-strength parameter estimation PoiGHL model illustrated as a reliable choice in reliability analysis as shown using two real data set.

scholarly journals Parametric and Semiparametric Estimations of Bivariate Truncated Type I Generalized Logistic Models driven from Copulas

2017 ◽  
Vol 7 (1) ◽  
pp. 72 ◽  
Author(s):  
Lamya A Baharith
Keyword(s):  
Logistic Models ◽  
Real Data ◽  
Information Criterion ◽  
Logistic Distribution ◽  
Type I ◽  
Copula Functions ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Generalized Logistic Distribution ◽  
Weibull Models

Truncated type I generalized logistic distribution has been used in a variety of applications. In this article, a new bivariate truncated type I generalized logistic (BTTGL) distributional models driven from three different copula functions are introduced. A study of some properties is illustrated. Parametric and semiparametric methods are used to estimate the parameters of the BTTGL models. Maximum likelihood and inference function for margin estimates of the BTTGL parameters are compared with semiparametric estimates using real data set. Further, a comparison between BTTGL, bivariate generalized exponential and bivariate exponentiated Weibull models is conducted using Akaike information criterion and the maximized log-likelihood. Extensive Monte Carlo simulation study is carried out for different values of the parameters and different sample sizes to compare the performance of parametric and semiparametric estimators based on relative mean square error.

3D stochastic gravity inversion using nonstationary covariances

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. G15-G24 ◽  
Author(s):  
Pejman Shamsipour ◽  
Denis Marcotte ◽  
Michel Chouteau ◽  
Martine Rivest ◽  
Abderrezak Bouchedda
Keyword(s):  
Real Data ◽  
Gravity Inversion ◽  
Data Set ◽  
The Real ◽  
Statistical Homogeneity ◽  
Nonstationary Covariance ◽  
Surface Geology ◽  
Synthetic Models ◽  
Stochastic Gravity

The flexibility of geostatistical inversions in geophysics is limited by the use of stationary covariances, which, implicitly and mostly for mathematical convenience, assumes statistical homogeneity of the studied field. For fields showing sharp contrasts due, for example, to faults or folds, an approach based on the use of nonstationary covariances for cokriging inversion was developed. The approach was tested on two synthetic cases and one real data set. Inversion results based on the nonstationary covariance were compared to the results from the stationary covariance for two synthetic models. The nonstationary covariance better recovered the known synthetic models. With the real data set, the nonstationary assumption resulted in a better match with the known surface geology.

Load-sharing system model and its application to the real data set

2012 ◽  
Vol 82 (9) ◽  
pp. 1615-1629 ◽  
Author(s):  
Bhupendra Singh ◽  
Puneet Kumar Gupta
Keyword(s):  
Real Data ◽  
Load Sharing ◽  
System Model ◽  
Data Set ◽  
The Real

A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution

2020 ◽  
Vol 17 (11) ◽  
pp. 4813-4818
Author(s):  
Sanaa Al-Marzouki ◽  
Sharifah Alrajhi
Keyword(s):  
Logistic Model ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Data Set ◽  
New Family ◽  
Probability Weighted Moment ◽  
The Subject ◽  
Generated Family ◽  
Family Of Distributions

We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals Robustness of Projective IRT to Misspecification of the Underlying Multidimensional Model

2020 ◽  
Vol 44 (5) ◽  
pp. 362-375
Author(s):  
Tyler Strachan ◽  
Edward Ip ◽  
Yanyan Fu ◽  
Terry Ackerman ◽  
Shyh-Huei Chen ◽  
...  
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Real Data ◽  
Model Parameters ◽  
Simulation Studies ◽  
Response Theory ◽  
Computational Stability ◽  
Data Set ◽  
Response Data ◽  
Higher Dimensional

As a method to derive a “purified” measure along a dimension of interest from response data that are potentially multidimensional in nature, the projective item response theory (PIRT) approach requires first fitting a multidimensional item response theory (MIRT) model to the data before projecting onto a dimension of interest. This study aims to explore how accurate the PIRT results are when the estimated MIRT model is misspecified. Specifically, we focus on using a (potentially misspecified) two-dimensional (2D)-MIRT for projection because of its advantages, including interpretability, identifiability, and computational stability, over higher dimensional models. Two large simulation studies (I and II) were conducted. Both studies examined whether the fitting of a 2D-MIRT is sufficient to recover the PIRT parameters when multiple nuisance dimensions exist in the test items, which were generated, respectively, under compensatory MIRT and bifactor models. Various factors were manipulated, including sample size, test length, latent factor correlation, and number of nuisance dimensions. The results from simulation studies I and II showed that the PIRT was overall robust to a misspecified 2D-MIRT. Smaller third and fourth simulation studies were done to evaluate recovery of the PIRT model parameters when the correctly specified higher dimensional MIRT or bifactor model was fitted with the response data. In addition, a real data set was used to illustrate the robustness of PIRT.

scholarly journals Monofractal or multifractal: a case study of spatial distribution of mining-induced seismic activity

1994 ◽  
Vol 1 (2/3) ◽  
pp. 182-190 ◽  
Author(s):  
M. Eneva
Keyword(s):  
Spatial Distribution ◽  
Seismic Activity ◽  
Real Data ◽  
Data Sets ◽  
Point Sets ◽  
Data Set ◽  
Limited Size ◽  
The Real ◽  
Induced Seismic Activity ◽  
Generalized Correlation

Abstract. Using finite data sets and limited size of study volumes may result in significant spurious effects when estimating the scaling properties of various physical processes. These effects are examined with an example featuring the spatial distribution of induced seismic activity in Creighton Mine (northern Ontario, Canada). The events studied in the present work occurred during a three-month period, March-May 1992, within a volume of approximate size 400 x 400 x 180 m3. Two sets of microearthquake locations are studied: Data Set 1 (14,338 events) and Data Set 2 (1654 events). Data Set 1 includes the more accurately located events and amounts to about 30 per cent of all recorded data. Data Set 2 represents a portion of the first data set that is formed by the most accurately located and the strongest microearthquakes. The spatial distribution of events in the two data sets is examined for scaling behaviour using the method of generalized correlation integrals featuring various moments q. From these, generalized correlation dimensions are estimated using the slope method. Similar estimates are made for randomly generated point sets using the same numbers of events and the same study volumes as for the real data. Uniform and monofractal random distributions are used for these simulations. In addition, samples from the real data are randomly extracted and the dimension spectra for these are examined as well. The spectra for the uniform and monofractal random generations show spurious multifractality due only to the use of finite numbers of data points and limited size of study volume. Comparing these with the spectra of dimensions for Data Set 1 and Data Set 2 allows us to estimate the bias likely to be present in the estimates for the real data. The strong multifractality suggested by the spectrum for Data Set 2 appears to be largely spurious; the spatial distribution, while different from uniform, could originate from a monofractal process. The spatial distribution of microearthquakes in Data Set 1 is either monofractal as well, or only weakly multifractal. In all similar studies, comparisons of result from real data and simulated point sets may help distinguish between genuine and artificial multifractality, without necessarily resorting to large number of data.

scholarly journals Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. M1-M10 ◽  
Author(s):  
Leonardo Azevedo ◽  
Ruben Nunes ◽  
Pedro Correia ◽  
Amílcar Soares ◽  
Luis Guerreiro ◽  
...  
Keyword(s):  
Multidimensional Scaling ◽  
Metric Space ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Algorithm ◽  
Data Set ◽  
The Real ◽  
Geostatistical Inversion ◽  
Impedance Models

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a cross-validation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.

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