scholarly journals Discriminating between the normal inverse Gaussian and generalized hyperbolic skew-t distributions with a follow-up the stock exchange data

2018 ◽  
Vol 28 (2) ◽  
pp. 185-199
Author(s):  
Hanieh Panahi
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Stock Exchange ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Information Criteria ◽  
Inverse Gaussian ◽  
Unknown Parameters ◽  
Normal Inverse Gaussian ◽  
Exchange Data

The statistical methods for the financial returns play a key role in measuring the goodness-of-fit of a given distribution to real data. As is well known, the normal inverse Gaussian (NIG) and generalized hyperbolic skew-t (GHST) distributions have been found to successfully describe the data of the returns from financial market. In this paper, we mainly consider the discrimination between these distributions. It is observed that the maximum likelihood estimators (MLEs) cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators. The approximate confidence intervals of the unknown parameters have been constructed. We then perform a number of goodness-of-fit tests to compare the NIG and GHST distributions for the stock exchange data. Moreover, the Vuong type test, based on the Kullback-Leibler information criteria, has been considered to select the most appropriate candidate model. An important implication of the present study is that the GHST distribution function, in contrast to NIG distribution, may describe more appropriate for the proposed data.

The exponentiated exponential burr XII distribution: Theory and application to lifetime data

2020 ◽  
pp. 1-14
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Significant Heterogeneity ◽  
Lifetime Data ◽  
Fit Statistics ◽  
Mathematical Properties ◽  
New Distribution

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.

scholarly journals Marshall-Olkin Lehmann Lomax Distribution: Theory, Statistical Properties, Copulas and Real Data Modeling

2021 ◽  
pp. 509-530
Author(s):  
Mohamed Aboraya
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Unknown Parameters ◽  
Clayton Copula ◽  
Lomax Distribution ◽  
Mean Squared Errors ◽  
Method Of Maximum Likelihood ◽  
Coefficient Of Skewness ◽  
New Distribution

In this work, a new four-parameter lifetime probability distribution called the Marshall-Olkin Lehmann Lomax distribution is defined and studied. The density function of the new distribution "asymmetric right skewed" and "symmetric" and the corresponding hazard rate can be monotonically increasing, increasing-constant, constant, upside down and monotonically decreasing. The coefficient of skewness can be negative and positive. We derive some new bivariate versions via Farlie Gumbel Morgenstern family, modified Farlie Gumbel Morgenstern family, Clayton Copula and Renyi's entropy.The method of maximum likelihood is used to estimate the unknown parameters. Using "biases" and "mean squared errors", a simulation study is performed for assessing the finite behavior of the maximum likelihood estimators.

scholarly journals The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties

2021 ◽  
Vol 11 (13) ◽  
pp. 6000
Author(s):  
Khalaf S. Sultan ◽  
Walid Emam
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Hybrid Censoring ◽  
Censored Samples ◽  
Distribution Estimation

In this paper, we use the combined-unified hybrid censoring samples to obtain the maximum likelihood estimates of the unknown parameters, survival, and hazard functions of Pareto distribution. Next, we discuss some efficiency criteria of the maximum likelihood estimators, including; the unbiasedness, consistency, and sufficiency. Additionally, we use MCMC to obtain the Bayesian estimates of the unknown parameters. In addition, we calculate the intervals estimation of the unknown parameters. Finally, we analyze a set of real data in view of the theoretical findings of the paper.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals Container Throughput Forecasting Using Dynamic Factor Analysis and ARIMAX Model

2017 ◽  
Vol 29 (5) ◽  
pp. 529-542 ◽  
Author(s):  
Marko Intihar ◽  
Tomaž Kramberger ◽  
Dejan Dragan
Keyword(s):  
Factor Analysis ◽  
Goodness Of Fit ◽  
Moving Average ◽  
Real Data ◽  
Information Criteria ◽  
Dynamic Factor Analysis ◽  
Forecasting Model ◽  
Dynamic Factor ◽  
Macroeconomic Indicators ◽  
The Impact

The paper examines the impact of integration of macroeconomic indicators on the accuracy of container throughput time series forecasting model. For this purpose, a Dynamic factor analysis and AutoRegressive Integrated Moving-Average model with eXogenous inputs (ARIMAX) are used. Both methodologies are integrated into a novel four-stage heuristic procedure. Firstly, dynamic factors are extracted from external macroeconomic indicators influencing the observed throughput. Secondly, the family of ARIMAX models of different orders is generated based on the derived factors. In the third stage, the diagnostic and goodness-of-fit testing is applied, which includes statistical criteria such as fit performance, information criteria, and parsimony. Finally, the best model is heuristically selected and tested on the real data of the Port of Koper. The results show that by applying macroeconomic indicators into the forecasting model, more accurate future throughput forecasts can be achieved. The model is also used to produce future forecasts for the next four years indicating a more oscillatory behaviour in (2018-2020). Hence, care must be taken concerning any bigger investment decisions initiated from the management side. It is believed that the proposed model might be a useful reinforcement of the existing forecasting module in the observed port.

scholarly journals Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su
Keyword(s):  
Nonlinear Diffusion ◽  
Goodness Of Fit ◽  
Real Data ◽  
Degradation Process ◽  
Copula Function ◽  
Assessment Method ◽  
Unknown Parameters ◽  
Degradation Data ◽  
Proposed Model ◽  
Frank Copula

A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

scholarly journals A New Extended-F Family: Properties and Applications to Lifetime Data

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Saima K. Khosa ◽  
Ahmed Z. Afify ◽  
Zubair Ahmad ◽  
Mi Zichuan ◽  
Saddam Hussain ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Model Parameters ◽  
Additional Parameter ◽  
Alpha Power ◽  
New Approach ◽  
New Class ◽  
Mathematical Properties ◽  
Extended Weibull Distribution

In this article, a new approach is used to introduce an additional parameter to a continuous class of distributions. The new class is referred to as a new extended-F family of distributions. The new extended-Weibull distribution, as a special submodel of this family, is discussed. General expressions for some mathematical properties of the proposed family are derived, and maximum likelihood estimators of the model parameters are obtained. Furthermore, a simulation study is provided to evaluate the validity of the maximum likelihood estimators. Finally, the flexibility of the proposed method is illustrated via two applications to real data, and the comparison is made with the Weibull and some of its well-known extensions such as Marshall–Olkin Weibull, alpha power-transformed Weibull, and Kumaraswamy Weibull distributions.

scholarly journals Generalized Truncation Positive Normal Distribution

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1361
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Data Sets ◽  
New Model ◽  
Positive Support

In this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model’s basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model’s good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption.

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