ARIMA model for forecasting of evaporation of Solapur station of Maharashtra, India

This paper deals with the stochastic modeling of weekly evaporation by using Seasonal ARIMA model for weekly evaporation data for the period of 1987-2008 with a total of 1144 readings for semi-arid Solapur station in Maharashtra. ARIMA models of 1st order were selected based on observing autocorrelation function (ACF) and partial autocorrelation function (PACF) of the weekly evaporation series. The model parameters were obtained by using maximum likelihood method with the help of three tests (i.e., standard error, ACF and PACF of residuals and Akaike Information Criteria). Adequacy of the selected models was determined. The ARIMA model that passed the adequacy test was selected for forecasting. The Seasonal ARIMA (1, 0, 1) (1, 0, 1)52 with lower RMSE is finally selected for forecasting of weekly evaporation values, at Solapur.

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Forecasting Rice Productivity and Production of Odisha, India, Using Autoregressive Integrated Moving Average Models

Advances in Agriculture ◽

10.1155/2014/621313 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Rahul Tripathi ◽

A. K. Nayak ◽

R. Raja ◽

Mohammad Shahid ◽

Anjani Kumar ◽

...

Keyword(s):

Autocorrelation Function ◽

Moving Average ◽

Selection Criterion ◽

Information Criteria ◽

Arima Models ◽

Autoregressive Integrated Moving Average ◽

Rice Productivity ◽

Rice Area ◽

Moving Average Models ◽

Partial Autocorrelation Function

Forecasting of rice area, production, and productivity of Odisha was made from the historical data of 1950-51 to 2008-09 by using univariate autoregressive integrated moving average (ARIMA) models and was compared with the forecasted all Indian data. The autoregressive (p) and moving average (q) parameters were identified based on the significant spikes in the plots of partial autocorrelation function (PACF) and autocorrelation function (ACF) of the different time series. ARIMA (2, 1, 0) model was found suitable for all Indian rice productivity and production, whereas ARIMA (1, 1, 1) was best fitted for forecasting of rice productivity and production in Odisha. Prediction was made for the immediate next three years, that is, 2007-08, 2008-09, and 2009-10, using the best fitted ARIMA models based on minimum value of the selection criterion, that is, Akaike information criteria (AIC) and Schwarz-Bayesian information criteria (SBC). The performances of models were validated by comparing with percentage deviation from the actual values and mean absolute percent error (MAPE), which was found to be 0.61 and 2.99% for the area under rice in Odisha and India, respectively. Similarly for prediction of rice production and productivity in Odisha and India, the MAPE was found to be less than 6%.

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A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽

10.3390/sym12030440 ◽

2020 ◽

Vol 12 (3) ◽

pp. 440 ◽

Cited By ~ 8

Author(s):

Abdulhakim A. Al-babtain ◽

I. Elbatal ◽

Haitham M. Yousof

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Data ◽

Likelihood Method ◽

Model Parameters ◽

Simple Type ◽

Data Sets ◽

New Model ◽

Clayton Copula ◽

Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

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Asymptotic properties of M-estimator for GARCH(1, 1) model parameters

Journal of the Belarusian State University. Mathematics and Informatics ◽

10.33581/2520-6508-2020-2-69-78 ◽

2020 ◽

pp. 69-78

Author(s):

Uladzimir S. Tserakh

Keyword(s):

Maximum Likelihood ◽

Heavy Tails ◽

Maximum Likelihood Method ◽

Asymptotic Properties ◽

Likelihood Method ◽

Model Parameters ◽

Economic Time Series ◽

Volatility Clustering ◽

Asymptotically Normal ◽

M Estimator

GARCH(1, 1) model is used for analysis and forecasting of financial and economic time series. In the classical version, the maximum likelihood method is used to estimate the model parameters. However, this method is not convenient for analysis of models with residuals distribution different from normal. In this paper, we consider M-estimator for the GARCH(1, 1) model parameters, which is a generalization of the maximum likelihood method. An algorithm for constructing an M-estimator is described and its asymptotic properties are studied. A set of conditions is formulated under which the estimator is strictly consistent and has an asymptotically normal distribution. This method allows to analyze models with different residuals distributions; in particular, models with stable and tempered stable distributions that allow to take into account the features of real financial data: volatility clustering, heavy tails, asymmetry.

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Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

International Journal of Statistics and Probability ◽

10.5539/ijsp.v10n3p8 ◽

2021 ◽

Vol 10 (3) ◽

pp. 8

Author(s):

Adebisi Ade Ogunde ◽

Gbenga Adelekan Olalude ◽

Oyebimpe Emmanuel Adeniji ◽

Kayode Balogun

Keyword(s):

Maximum Likelihood ◽

Poisson Distribution ◽

Maximum Likelihood Method ◽

Life Time ◽

Real Data ◽

Likelihood Method ◽

Strength Parameter ◽

Model Parameters ◽

Type Ii ◽

Time Data

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

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Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications

Symmetry ◽

10.3390/sym11121459 ◽

2019 ◽

Vol 11 (12) ◽

pp. 1459 ◽

Cited By ~ 3

Author(s):

Ramadan A. ZeinEldin ◽

Farrukh Jamal ◽

Christophe Chesneau ◽

Mohammed Elgarhy

Keyword(s):

Maximum Likelihood ◽

Probability Density ◽

Goodness Of Fit ◽

Maximum Likelihood Method ◽

Information Criteria ◽

Likelihood Method ◽

Type Ii ◽

Asymptotic Results ◽

Kumaraswamy Distribution ◽

New Distribution

In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics.

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A New Family of Continuous Probability Distributions

Entropy ◽

10.3390/e23020194 ◽

2021 ◽

Vol 23 (2) ◽

pp. 194

Author(s):

M. El-Morshedy ◽

Fahad Sameer Alshammari ◽

Yasser S. Hamed ◽

Mohammed S. Eliwa ◽

Haitham M. Yousof

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Probability Distributions ◽

Real Life ◽

Likelihood Method ◽

Model Parameters ◽

Finite Sample ◽

Graphical Simulation ◽

New Family ◽

The One

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

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Estimasi Parameter Model Autoregressive dengan Metode Yule Walker, Least Square, dan Maximum Likelihood (Studi Kasus Data ROA BPRS di Indonesia)

Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education ◽

10.14421/quadratic.2021.011-01 ◽

2021 ◽

Vol 1 (1) ◽

pp. 1-6

Author(s):

Maulida Nurhidayati

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Least Square ◽

Likelihood Method ◽

Model Parameters ◽

Likelihood Methods ◽

Simulation Data ◽

Sample Data ◽

Maximum Likelihood Methods ◽

Modeling Data

The Autoregressive model is a time series univariate model for stationary models. In estimating parameters on this model can be done by several methods, namely yule-walker method, Least Square, and Maximum Likelihood. Each method has a different principle for estimating model parameters so that the results obtained will also be different. Based on this, in this study, the AR(1) model parameter estimation was estimated by generating data simulated 1000 times to see the performance of Yule-Walker, Least Square, and Maximum Likelihood methods. In addition, the comparison of these three methods is also done on ROA BPRS data that follows the AR(1) model. The results showed that the Maximum Likelihood method was able to provide mode results and comparison of the most suitable estimation results for simulation data and produce the smallest MAE values in the data in sample and MAPE, MSE, and MAE the smallest in the out sample data. These results show that the Maximum Likelihood method is the best method for modeling data that follows the AR(1) model.

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An algorithm for the assessment of several small rates

Lietuvos matematikos rinkinys ◽

10.15388/lmr.b.2012.47 ◽

2012 ◽

Vol 53 ◽

Author(s):

Leonidas Sakalauskas ◽

Ingrida Vaičiulytė

Keyword(s):

Maximum Likelihood ◽

Bayesian Approach ◽

Maximum Likelihood Method ◽

Rare Events ◽

Maximum Likelihood Estimates ◽

Likelihood Method ◽

Model Parameters ◽

Unknown Parameters ◽

Empirical Bayesian ◽

Empirical Bayesian Approach

The present paper describes the empirical Bayesian approach applied in the estimation of several small rates. Modeling by empirical Bayesian approach the probabilities of several rare events, it is assumed that the frequencies of events follow to Poisson’s law with different parameters, which are correlated Gaussian random values. The unknown parameters are estimated by the maximum likelihood method computing the integrals appeared here by Hermite–Gauss quadratures. The equations derived that are satisfied by maximum likelihood estimates of model parameters.

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New Extension of Weibull Distribution: Copula, Mathematical Properties and Data Modeling

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-1036 ◽

2020 ◽

Vol 8 (4) ◽

pp. 972-993

Author(s):

Hanaa Elgohari ◽

Haitham Yousof

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Likelihood Estimation ◽

Likelihood Method ◽

Model Parameters ◽

Graphical Simulation ◽

Mathematical Properties ◽

Exponentiated Weibull ◽

Lifetime Model ◽

Simulation Results

This paper introduces a new flexible four-parameter lifetime model. Various of its structural properties are derived. The new density is expressed as a linear mixture of well-known exponentiated Weibull density. The maximum likelihood method is used to estimate the model parameters. Graphical simulation results to assess the performance of the maximum likelihood estimation are performed. We proved empirically the importance and flexibility of the new model in modeling four various types of data.

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The Modified Beta Gompertz Distribution: Theory and Applications

Mathematics ◽

10.3390/math7010003 ◽

2018 ◽

Vol 7 (1) ◽

pp. 3

Author(s):

Ibrahim Elbatal ◽

Farrukh Jamal ◽

Christophe Chesneau ◽

Mohammed Elgarhy ◽

Sharifah Alrajhi

Keyword(s):

Maximum Likelihood ◽

Probability Distribution ◽

Simulation Study ◽

Maximum Likelihood Method ◽

Maximum Likelihood Estimators ◽

Quantile Function ◽

Moment Generating Function ◽

Likelihood Method ◽

Model Parameters ◽

Gompertz Distribution

In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomena. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, entropies and order statistics. We explore the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study testing the validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by the consideration of two real datasets.

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