A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models

2020 ◽  
Vol 70 (4) ◽  
pp. 979-994
Author(s):  
Emrah Altun
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Count Data ◽  
Discrete Distribution ◽  
Real Data ◽  
Autoregressive Process ◽  
Important Application ◽  
Statistical Properties ◽  
Data Sets ◽  
Application Fields

AbstractThis study introduces the Poisson-Bilal distribution and its associated two models for modeling the over-dispersed count data sets. The Poisson-Bilal distribution has tractable properties and explicit forms for its statistical properties. A new over-dispersed count regression model and integer-valued autoregressive process with flexible innovation distribution are defined and studied comprehensively. Two real data sets are analyzed to prove empirically the importance of proposed models. Empirical findings show that the Poisson-Bilal distribution has important application fields in time series and regression modeling.

scholarly journals A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

2022 ◽  
Vol 7 (2) ◽  
pp. 1726-1741
Author(s):  
Ahmed Sedky Eldeeb ◽  
◽  
Muhammad Ahsan-ul-Haq ◽  
Mohamed. S. Eliwa ◽  
◽  
...  
Keyword(s):  
Count Data ◽  
Discrete Distribution ◽  
Real Data ◽  
Mass Function ◽  
Probability Mass Function ◽  
Data Sets ◽  
Estimation Techniques ◽  
Proposed Model ◽  
Probability Mass ◽  
Von Mises

<abstract> <p>In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical and reliability properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.</p> </abstract>

scholarly journals The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

scholarly journals A Note on the Properties of Generalised Separable Spatial Autoregressive Process

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Mahendran Shitan ◽  
Shelton Peiris
Keyword(s):  
Three Dimensional ◽  
Real Data ◽  
Autoregressive Process ◽  
Spatial Modelling ◽  
Spectral Density Function ◽  
Data Sets ◽  
Additional Parameter ◽  
New Class ◽  
Spatial Autoregressive ◽  
Modelling And Forecasting

Spatial modelling has its applications in many fields like geology, agriculture, meteorology, geography, and so forth. In time series a class of models known as Generalised Autoregressive (GAR) has been introduced by Peiris (2003) that includes an index parameterδ. It has been shown that the inclusion of this additional parameter aids in modelling and forecasting many real data sets. This paper studies the properties of a new class of spatial autoregressive process of order 1 with an index. We will call this aGeneralised Separable Spatial Autoregressive(GENSSAR) Model. The spectral density function (SDF), the autocovariance function (ACVF), and the autocorrelation function (ACF) are derived. The theoretical ACF and SDF plots are presented as three-dimensional figures.

Anomalies and False Rejections

2020 ◽  
Vol 33 (5) ◽  
pp. 2134-2179 ◽  
Author(s):  
Tarun Chordia ◽  
Amit Goyal ◽  
Alessio Saretto
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Real Data ◽  
Multiple Hypothesis Testing ◽  
Statistical Properties ◽  
Trading Strategies ◽  
Cross Sectional ◽  
Publication Process ◽  
Multiple Hypothesis ◽  
Expected Proportion

Abstract We use information from over 2 million trading strategies randomly generated using real data and from strategies that survive the publication process to infer the statistical properties of the set of strategies that could have been studied by researchers. Using this set, we compute $t$-statistic thresholds that control for multiple hypothesis testing, when searching for anomalies, at 3.8 and 3.4 for time-series and cross-sectional regressions, respectively. We estimate the expected proportion of false rejections that researchers would produce if they failed to account for multiple hypothesis testing to be about 45%.

scholarly journals A New Strategy of Hybrid Models using ARIMA, ANN, and DWT in Time Series Modelling

2021 ◽  
Vol 25 (1) ◽  
pp. 27-50
Author(s):  
Tsung-Lin Li ◽  
◽  
Chen-An Tsai ◽  
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Arima Model ◽  
Real Data ◽  
Hybrid Models ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Model Combining ◽  
Time Series Modelling ◽  
Significant Difference

Time series forecasting is a challenging task of interest in many disciplines. A variety of techniques have been developed to deal with the problem through a combination of different disciplines. Although various researches have proved successful for hybrid models, none of them carried out the comparisons with solid statistical test. This paper proposes a new stepwise model determination method for artificial neural network (ANN) and a novel hybrid model combining autoregressive integrated moving average (ARIMA) model, ANN and discrete wavelet transformation (DWT). Simulation studies are conducted to compare the performance of different models, including ARIMA, ANN, ARIMA-ANN, DWT-ARIMA-ANN and the proposed method, ARIMA-DWT-ANN. Also, two real data sets, Lynx data and cabbage data, are used to demonstrate the applications. Our proposed method, ARIMA-DWT-ANN, outperforms other methods in both simulated datasets and Lynx data, while ANN shows a better performance in the cabbage data. We conducted a two-way ANOVA test to compare the performances of methods. The results showed a significant difference between methods. As a brief conclusion, it is suggested to try on ANN and ARIMA-DWT-ANN due to their robustness and high accuracy. Since the performance of hybrid models may vary across data sets based on their ARIMA alike or ANN alike natures, they should all be considered when encountering a new data to reach an optimal performance.

scholarly journals Geometric Regression for Modelling Count Data on the Time-to-First Antenatal Care Visit

2020 ◽  
Vol 23 (1) ◽  
pp. 35-57
Author(s):  
Zainab Mohammed Darwish Al-Balushi ◽  
◽  
M. Mazharul Islam ◽  
Keyword(s):  
Antenatal Care ◽  
Regression Model ◽  
Count Data ◽  
Negative Binomial ◽  
Geometric Distribution ◽  
Discrete Distribution ◽  
Mass Function ◽  
Probability Mass Function ◽  
Antenatal Care Visit ◽  
Care Visit

Geometric distribution belongs to the family of discrete distribution that deals with the count of trail needed for first occurrence or success of any event. However, little attention has been paid in applying the GLM for the geometric distribution, which has a very simple form for its probability mass function with a single parameter. In this study, an attempt has been made to introduce geometric regression for modelling the count data. We have illustrated the suitability of the geometric regression model for analyzing the count data on time to first antenatal care visit that displayed under-dispersion, and the results were compared with Poisson and negative binomial regressions. We conclude that the geometric regression model may provide a flexible model for fitting count data sets which may present over-dispersion or under-dispersion, and the model may serve as an alternative model to the very familiar Poisson and negative binomial models for modelling count data.

scholarly journals Time series forecasting of styrene price using a hybrid ARIMA and neural network model

2019 ◽  
Vol 10 (3) ◽  
pp. 915
Author(s):  
Ali Ebrahimi Ghahnavieh
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Real Data ◽  
Time Series Forecasting ◽  
Series Data ◽  
Data Sets ◽  
Combined Model ◽  
Future Behavior ◽  
Hybrid Forecasting ◽  
Ann Models

Every player in the market has a greater need to know about the smallest change in the market. Therefore, the ability to see what is ahead is a valuable advantage. The purpose of this research is to make an attempt to understand the behavioral patterns and try to find a new hybrid forecasting approach based on ARIMA-ANN for estimating styrene price. The time series analysis and forecasting is an essential tool which could be widely useful for finding the significant characteristics for making future decisions. In this study ARIMA, ANN and Hybrid ARIMA-ANN models were applied to evaluate the previous behavior of a time series data, in order to make interpretations about its future behavior for styrene price. Experimental results with real data sets show that the combined model can be most suitable to improve forecasting accurateness rather than traditional time series forecasting methodologies. As a subset of the literature, the small number of studies have been done to realize the new forecasting methods for forecasting styrene price.

Stochastic Modeling of Time Series with Application to Local Damage Detection in Rotating Machinery

2013 ◽  
Vol 569-570 ◽  
pp. 441-448 ◽  
Author(s):  
Jakub Obuchowski ◽  
Agnieszka Wylomanska ◽  
Radoslaw Zimroz
Keyword(s):  
Time Series ◽  
Good Condition ◽  
Real Data ◽  
Statistical Properties ◽  
Normal Operation ◽  
Local Damage ◽  
Data Set ◽  
Time Frequency ◽  
Frequency Map ◽  
Vibration Time

Raw vibration signals measured on the machine housing in industrial conditions are complex and can be modeled as an additive mixture of several processes (with different statistical properties) related to normal operation of machine, damage related to one (or more) of its part, some noise, etc. In the case of local damage in rotating machines, contribution of informative process related to damage is hidden in the raw signal so its detection is difficult. In this paper we propose to use the statistical modeling of vibration time series to identify these components. Building the model of raw signal may be ineffective. It is proposed to decompose signal into set of narrowband sub-signals using time-frequency representation. Next, it is proposed to model each sub-signal in the given frequency range and classify all signals using their statistical properties. We have used several parameters (called selectors because they will be used for selection of sub-signals from time-frequency map for further processing) for analysis of sub-signals. They have base in statistics theory and can be useful for example in testing of normality of data set (vibration time series from machine in good condition is close to Gaussian, damaged not). Results of such modeling will be used in the sub-signals classification procedure but also in defects detection. We illustrate effectiveness of novel technique using real data from heavy machinery system.

scholarly journals A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 32-47
Author(s):  
Gauss Cordeiro ◽  
Maria de Lima ◽  
Edwin Ortega ◽  
Adriano Suzuki
Keyword(s):  
Maximum Likelihood ◽  
Regression Model ◽  
Real Data ◽  
Random Variable ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Poisson Random Variable ◽  
Fatigue Lifetime ◽  
Special Cases ◽  
New Distribution

We propose an extended fatigue lifetime model called the odd log-logistic Birnbaum–Saunders–Poisson distribution, which includes as special cases the Birnbaum–Saunders and odd log-logistic Birnbaum–Saunders distributions. We obtain some structural properties of the new distribution. We define a new extended regression model based on the logarithm of the odd log-logistic Birnbaum–Saunders–Poisson random variable. For censored data, we estimate the parameters of the regression model using maximum likelihood. We investigate the accuracy of the maximum likelihood estimates using Monte Carlo simulations. The importance of the proposed models, when compared to existing models, is illustrated by means of two real data sets.

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