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Journal articles on the topic 'Asymmetric exponential power distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Zhu, Dongming, and Victoria Zinde-Walsh. "Properties and estimation of asymmetric exponential power distribution." Journal of Econometrics 148, no. 1 (January 2009): 86–99. http://dx.doi.org/10.1016/j.jeconom.2008.09.038.

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2

Çankaya, Mehmet. "Asymmetric Bimodal Exponential Power Distribution on the Real Line." Entropy 20, no. 1 (January 3, 2018): 23. http://dx.doi.org/10.3390/e20010023.

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3

Baharith, Lamya A., and Wedad H. Aljuhani. "New Method for Generating New Families of Distributions." Symmetry 13, no. 4 (April 20, 2021): 726. http://dx.doi.org/10.3390/sym13040726.

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This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

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4

Olosunde, A. A., and A. T. Soyinka. "Interval Estimation for Symmetric and Asymmetric Exponential Power Distribution Parameters." Journal of the Iranian Statistical Society 18, no. 1 (June 1, 2019): 237–52. http://dx.doi.org/10.29252/jirss.18.1.237.

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5

Naranjo, L., C. J. Pérez, and J. Martín. "Bayesian analysis of some models that use the asymmetric exponential power distribution." Statistics and Computing 25, no. 3 (February 6, 2014): 497–514. http://dx.doi.org/10.1007/s11222-014-9449-1.

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6

Nadarajah, Saralees, and Mahdi Teimouri. "On the Characteristic Function for Asymmetric Exponential Power Distributions." Econometric Reviews 31, no. 4 (July 2012): 475–81. http://dx.doi.org/10.1080/07474938.2011.608000.

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7

Kurmankozhayev, Azimkhan, and Guldana Syzdykova. "EVALUATION OF EXTREMELY ASYMMETRIC TYPES OF DISTRIBUTIONS OF GEOFEATURES VALUES." Geodesy and Cartography 41, no. 3 (October 6, 2015): 131–36. http://dx.doi.org/10.3846/20296991.2015.1086127.

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Statistical and geometric patterns were disclosed that are inherent to extremely asymmetric types of formation of stochastic frequencies of geofeatures values with the help of the exponential, probabilistic, structural, and Zipf distribution laws, which are most often used to describe them. A sophisticated pattern with exponential and hyperbolic nature of the probabilistic frequencies formation development was found. Based on these features, a leading concept of using major structure-forming characteristics of the distribu- tion of variable parameters as desired theoretical distribution function was used for parameterization of an extremely asymmetric distribution model. A median and modal frequency of geofeatures distribution were defined as the theoretical parameters of the desired distribution model. A structure was constructed and formulas were derived for determination of the statistical characteristics of the recommended distribution model. Approbation of the distribution model was conducted on an example of morphometric signs empirical distributions among the localities of varying complexity and qualitative indicators of a number of gold and rare metal deposits; inhesion of its approxi- mating power and flexibility of use was revealed.

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8

Li, Zhimin, Zhaolin He, and Chunhua Hu. "Asymptotic Degree Distribution of a Kind of Asymmetric Evolving Network." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/761235.

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We propose a kind of evolving network which shows tree structure. The model is a combination of preferential attachment model and uniform model. We show that the proportional degree sequencepkk>1obeys power law, exponential distribution, and other forms according to the relation ofkand parameterm.

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9

Klakattawi, Hadeel S., and Wedad H. Aljuhani. "A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family." Symmetry 13, no. 3 (March 4, 2021): 412. http://dx.doi.org/10.3390/sym13030412.

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In the following article, a new five-parameter distribution, the alpha power exponentiated Weibull-exponential distribution is proposed, based on a newly developed technique. It is of particular interest because the density of this distribution can take various symmetric and asymmetric possible shapes. Moreover, its related hazard function is tractable and showing a great diversity of asymmetrical shaped, including increasing, decreasing, near symmetrical, increasing-decreasing-increasing, increasing-constant-increasing, J-shaped, and reversed J-shaped. Some properties relating to the proposed distribution are provided. The inferential method of maximum likelihood is employed, in order to estimate the model’s unknown parameters, and these estimates are evaluated based on various simulation studies. Moreover, the usefulness of the model is investigated through its application to three real data sets. The results show that the proposed distribution can, in fact, better fit the data, when compared to other competing distributions.

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10

Olmos, Neveka M., Osvaldo Venegas, Yolanda M. Gómez, and Yuri A. Iriarte. "An Asymmetric Distribution with Heavy Tails and Its Expectation–Maximization (EM) Algorithm Implementation." Symmetry 11, no. 9 (September 10, 2019): 1150. http://dx.doi.org/10.3390/sym11091150.

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In this paper we introduce a new distribution constructed on the basis of the quotient of two independent random variables whose distributions are the half-normal distribution and a power of the exponential distribution with parameter 2 respectively. The result is a distribution with greater kurtosis than the well known half-normal and slashed half-normal distributions. We studied the general density function of this distribution, with some of its properties, moments, and its coefficients of asymmetry and kurtosis. We developed the expectation–maximization algorithm and present a simulation study. We calculated the moment and maximum likelihood estimators and present three illustrations in real data sets to show the flexibility of the new model.

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11

Picard, Nicolas. "Asymmetric Competition Can Shape the Size Distribution of Trees in a Natural Tropical Forest." Forest Science 65, no. 5 (May 31, 2019): 562–69. http://dx.doi.org/10.1093/forsci/fxz018.

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Abstract The architecture (here, the size distribution combined with the spatial pattern of individuals) of natural forest at demographic equilibrium can be used to infer the demographic processes that drive the forest dynamics. In particular, a constant growth rate and a constant mortality rate for all trees would generate an exponential distribution of their size, whereas the metabolic scaling theory predicts a power distribution. In an undisturbed tropical rainforest in French Guiana, the diameter distribution was significantly steeper than the best-fit exponential distribution and significantly flatter than the best-fit power distribution. A simple individual-based model of forest dynamics with asymmetric competition between trees, where the strength of competition was regulated by a single parameter, was able to predict the observed distribution. Competition drove the forest into a self-organized state with stronger inequalities of size among trees, a lower mean competition index, and a spatial pattern of trees that deviated from complete spatial randomness.

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12

Fusek, Michal. "On Testing Reduction of Left-Censored Weibull Distribution to Exponential Submodel." MENDEL 23, no. 1 (June 1, 2017): 179–84. http://dx.doi.org/10.13164/mendel.2017.1.179.

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When analyzing environmental or chemical data, it is often necessary to deal with left-censoredobservations. Since the distribution of the observed variable is often asymmetric, the exponential or the Weibulldistribution can be used. This paper summarizes statistical model of a multiply left-censored Weibull distribution,and estimation of its parameters and their variances using the expected Fisher information matrix. Since inmany situations the Weibull distribution is unnecessarily complicated for data modelling, statistical tests (theLagrange multiplier test, the likelihood ratio test, the Wald test) for assessing suitability of replacement ofthe censored Weibull distribution with the exponential submodel are introduced and their power functions areanalyzed using simulations.

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13

Barakat, Haroon Mohamed, Osama Mohareb Khaled, and Nourhan Khalil Rakha. "Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization." Symmetry 12, no. 11 (November 14, 2020): 1876. http://dx.doi.org/10.3390/sym12111876.

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Several new asymmetric distributions have arisen naturally in the modeling extreme values are uncovered and elucidated. The present paper deals with the extreme value theorem (EVT) under exponential normalization. An estimate of the shape parameter of the asymmetric generalized value distributions that related to this new extension of the EVT is obtained. Moreover, we develop the mathematical modeling of the extreme values by using this new extension of the EVT. We analyze the extreme values by modeling the occurrence of the exceedances over high thresholds. The natural distributions of such exceedances, new four generalized Pareto families of asymmetric distributions under exponential normalization (GPDEs), are described and their properties revealed. There is an evident symmetry between the new obtained GPDEs and those generalized Pareto distributions arisen from EVT under linear and power normalization. Estimates for the extreme value index of the four GPDEs are obtained. In addition, simulation studies are conducted in order to illustrate and validate the theoretical results. Finally, a comparison study between the different extreme models is done throughout real data sets.

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14

PELLICER-LOSTAO, CARMEN, and RICARDO LOPEZ-RUIZ. "TRANSITION FROM EXPONENTIAL TO POWER LAW INCOME DISTRIBUTIONS IN A CHAOTIC MARKET." International Journal of Modern Physics C 22, no. 01 (January 2011): 21–33. http://dx.doi.org/10.1142/s0129183111016038.

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Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

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15

Zhu, Dongming, and John W. Galbraith. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions." Journal of Empirical Finance 18, no. 4 (September 2011): 765–78. http://dx.doi.org/10.1016/j.jempfin.2011.05.006.

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16

Asquith, William H. "Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R." Computational Statistics & Data Analysis 71 (March 2014): 955–70. http://dx.doi.org/10.1016/j.csda.2012.12.013.

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17

Delicado, P., and M. N. Goria. "A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution." Computational Statistics & Data Analysis 52, no. 3 (January 2008): 1661–73. http://dx.doi.org/10.1016/j.csda.2007.05.021.

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18

Lee, Sangyeol, and Minjo Kim. "On entropy-based goodness-of-fit test for asymmetric Student-t and exponential power distributions." Journal of Statistical Computation and Simulation 87, no. 1 (June 13, 2016): 187–97. http://dx.doi.org/10.1080/00949655.2016.1196690.

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19

Yang, Xianzi, Chen Zhang, Yu Yang, Yaqi Wu, Po Yun, and Zulfiqar Ali Wagan. "China’s Carbon Pricing Based on Heterogeneous Tail Distribution." Sustainability 12, no. 7 (April 1, 2020): 2754. http://dx.doi.org/10.3390/su12072754.

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To address climate change, the carbon emission trading scheme has become one of the main measures to achieve emission reduction goals. One of the core problems in constructing the carbon emissions trading market is determining carbon emissions trading prices. The scientific nature of carbon emissions pricing determines the effectiveness of market regulation. Research on the influencing factors and heterogeneous tail distribution of carbon prices can increase the accuracy of carbon pricing, which is particularly important for the development of the carbon emissions trading market. The current studies have some limitations and lack heterogeneous tail description. We employ the arbitrage pricing theory-standardized standard asymmetric exponential power distribution model to analyze China’s regional carbon emissions trading price and use a genetic algorithm to solve linear programming. The results confirm the theoretical results and efficiency of the proposed algorithm. First, the new model can capture the skewness, fat-tailed distribution, and asymmetric effects of China’s regional carbon emissions trading price. Second, the macroeconomy, similar products, energy price, and exchange rate influence the carbon price fluctuation; investors’ behavior plays an important role in the heterogeneous tail distribution of carbon price. The findings provide references for the government to take appropriate measures to promote carbon emission reduction and improve the effectiveness of China’s carbon market. Therefore, our findings can help enhance emission reduction and achieve sustainable development of a low-carbon environment.

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20

Bantan, Rashad A. R., Farrukh Jamal, Christophe Chesneau, and Mohammed Elgarhy. "Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications." Symmetry 12, no. 1 (January 2, 2020): 75. http://dx.doi.org/10.3390/sym12010075.

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In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

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21

Astorga, Juan M., Jimmy Reyes, Karol I. Santoro, Osvaldo Venegas, and Héctor W. Gómez. "A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function." Mathematics 8, no. 9 (September 8, 2020): 1537. http://dx.doi.org/10.3390/math8091537.

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This article introduces an extension of the Power Muth (PM) distribution for modeling positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis than the PM distribution. We show that the density can be represented based on the incomplete generalized integro-exponential function. We study some of its properties and moments, and its coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum likelihood methods and present a simulation study to illustrate parameter recovery. The results of application to two real data sets indicate that the new model performs very well in the presence of outliers.

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22

Ojirobe, Yunusa Adavi, Abdulsalam Hussein Ahmad, and Ikwuoche John David. "Modelling and Forecasting Volatility of Crude Oil Returns in Nigeria based on Six Error Innovations." Journal of Statistical Modelling and Analytics 3, no. 1 (July 1, 2021): 78–93. http://dx.doi.org/10.22452/josma.vol3no1.6.

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Modeling price volatility of crude oil (PVCO) is pertinent because of the overbearing impact on any oil-producing economy. This study aimed at evaluating the performance of some volatility models in modeling and forecasting crude oil returns. Utilizing daily returns data from October 23, 2009, to March 23, 2020, this study attempted to capture the dynamics of crude oil price volatility in Nigeria using a symmetric and asymmetric GARCH models. In our research, we considered the generalized autoregressive conditional heteroscedastic model (GARCH), Exponential (E-GARCH), Glosten, Jagannathan and Runkle (GJR-GARCH) and Asymmetric Power (AP-ARCH) under six error innovations that include the skewed variant of the student-t, generalized error and normal distribution. From the results obtained, it was discovered that the AP-ARCH (1, 1) model performed better in the fitting and performance evaluation phase. The skew Student’s t-distribution (SStD) was also reported to be the best performing error innovation in most of the models. Based upon these results, we conclude that the AP-ARCH (1, 1)-SStD model is the best model for capturing the dynamics of crude oil returns in Nigeria.

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23

Godet, Christian. "Entropy effects in the collective dynamic behavior of alkyl monolayers tethered to Si(111)." Beilstein Journal of Nanotechnology 6 (February 26, 2015): 583–94. http://dx.doi.org/10.3762/bjnano.6.60.

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Dynamic properties of n-alkyl monolayers covalently bonded to Si(111) were studied by broadband admittance spectroscopy as a function of the temperature and the applied voltage using rectifying Hg/C12H25/n-type Si junctions. Partial substitution of methyl end groups by polar (carboxylic acid) moieties was used to enhance the chain end relaxation response. Two thermally activated dissipation mechanisms (B1 and B2, with f B1 < f B2) are evidenced for all reverse bias values. The strong decrease of both relaxation frequencies with increasing reverse dc bias reveals increasing motional constraints, attributed to electrostatic pressure applied to the densely-packed nanometer-thick monolayer. Spectral decomposition of the frequency response shows a power-law dependence of their activation energies on |V DC|. A large reverse bias reversibly increases the B2 response attributed to the distribution of gauche defects, in contrast with the constant strength of the acid dipole loss (B1). A trans–gauche isomerization energy of 50 meV is derived from the temperature dependence of the B2 dipolar strength. For both dissipation mechanisms, the observed linear correlation between activation energy and logarithm of pre-exponential factor is consistent with a multi-excitation entropy model, in which the molecular reorientation path is strongly coupled with a large number of low energy excitations (here the n-alkyl bending vibrational mode) collected from the thermal bath. This collective dynamic behavior of alkyl chains tethered to Si is also confirmed by the asymmetric relaxation peak shape related to many-body interactions in complex systems.

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24

SARAÇOĞLU, Buğra, and Caner TANIŞ. "A new lifetime distribution: transmuted exponential power distribution." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 70, no. 1 (January 1, 2021): 1–14. http://dx.doi.org/10.31801/cfsuasmas.528306.

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25

Flores D., José, Patrick Borges, Vicente G. Cancho, and Francisco Louzada. "The complementary exponential power series distribution." Brazilian Journal of Probability and Statistics 27, no. 4 (November 2013): 565–84. http://dx.doi.org/10.1214/11-bjps182.

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26

Mutlk, Rana Hadi, and Awatif Rezzoky Al-Dubaicy. "Even Power Weighted Generalized Exponential Distribution." Journal of Physics: Conference Series 1963, no. 1 (July 1, 2021): 012082. http://dx.doi.org/10.1088/1742-6596/1963/1/012082.

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27

Assar, Salwa Mahmoud. "On Odds Generalized Exponential-Power Lomax Distribution." Journal of Mathematics and Statistics 14, no. 1 (January 1, 2018): 167–74. http://dx.doi.org/10.3844/jmssp.2018.167.174.

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28

Hutson, Alan D. "An alternative skew exponential power distribution formulation." Communications in Statistics - Theory and Methods 48, no. 12 (November 22, 2018): 3005–24. http://dx.doi.org/10.1080/03610926.2018.1473600.

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29

Koh, Viroy C., and Lawrence M. Leemis. "Statistical procedures for the exponential power distribution." Microelectronics Reliability 29, no. 2 (January 1989): 227–36. http://dx.doi.org/10.1016/0026-2714(89)90570-2.

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30

Love, J. J., and J. L. Gannon. "Revised <I>D<sub>st</sub></I> and the epicycles of magnetic disturbance: 1958–2007." Annales Geophysicae 27, no. 8 (August 11, 2009): 3101–31. http://dx.doi.org/10.5194/angeo-27-3101-2009.

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Abstract. A revised version of the storm-time disturbance index Dst is calculated using hourly-mean magnetic-observatory data from four standard observatories and collected over the years 1958–2007. The calculation algorithm is a revision of that established by Sugiura et al., and which is now used by the Kyoto World Data Center for routine production of Dst. The most important new development is for the removal of solar-quiet variation. This is done through time and frequency-domain band-stop filtering – selectively removing specific Fourier terms approximating stationary periodic variation driven by the Earth's rotation, the Moon's orbit, the Earth's orbit around the Sun, and their mutual coupling. The resulting non-stationary disturbance time series are weighted by observatory-site geomagnetic latitude and then averaged together across longitudes to give what we call Dst5807-4SH. Comparisons are made with the standard Kyoto Dst. Various biases, especially for residual solar-quiet variation, are identified in the Kyoto Dst, and occasional storm-time errors in the Kyoto Dst are noted. Using Dst5807-4SH, storms are ranked for maximum storm-time intensity, and we show that storm-occurrence frequency follows a power-law distribution with an exponential cutoff. The epicycles of magnetic disturbance are explored: we (1) map low-latitude local-time disturbance asymmetry, (2) confirm the 27-day storm-recurrence phenomenon using autocorrelation, (3) investigate the coupled semi-annual-diurnal variation of magnetic activity and the proposed explanatory equinoctial and Russell-McPherron hypotheses, and (4) illustrate the well-known solar-cycle modulation of storm-occurrence likelihood. Since Dst5807-4SH is useful for a variety of space physics and solid-Earth applications, it is made freely available to the scientific community.

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31

Joshi, Ramesh Kumar. "Lindley Exponential Power Distribution with Properties and Applications." International Journal for Research in Applied Science and Engineering Technology 8, no. 10 (October 31, 2020): 22–30. http://dx.doi.org/10.22214/ijraset.2020.31743.

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32

TANIŞ, Caner, Buğra SARAÇOĞLU, Coşkun KUŞ, and Ahmet PEKGÖR. "Transmuted Complementary Exponential Power Distribution: Properties and Applications." Cumhuriyet Science Journal 41, no. 2 (June 25, 2020): 419–32. http://dx.doi.org/10.17776/csj.664757.

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33

Shparlinski, Igor E. "Distribution of exponential functions modulo a prime power." Journal of Number Theory 143 (October 2014): 224–31. http://dx.doi.org/10.1016/j.jnt.2014.04.010.

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34

Choy, S. T. Boris, and Stephen G. Walker. "The extended exponential power distribution and Bayesian robustness." Statistics & Probability Letters 65, no. 3 (November 2003): 227–32. http://dx.doi.org/10.1016/j.spl.2003.01.001.

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35

DiCiccio, Thomas J., and Anna Clara Monti. "Inferential Aspects of the Skew Exponential Power Distribution." Journal of the American Statistical Association 99, no. 466 (June 2004): 439–50. http://dx.doi.org/10.1198/016214504000000359.

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36

Zabolotnii, S. V., A. V. Chepynoha, Yu Yu Bondarenko, and M. P. Rud. "Polynomial parameter estimation of exponential power distribution data." Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, no. 75 (December 30, 2018): 40–47. http://dx.doi.org/10.20535/radap.2018.75.40-47.

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37

Ghitany, M. E., S. M. Aboukhamseen, and E. A. S. Mohammad. "Weighted half exponential power distribution and associated inference." Applied Mathematical Sciences 10 (2016): 91–108. http://dx.doi.org/10.12988/ams.2016.511696.

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38

Tumlinson, S. E., J. P. Keating, and N. Balakrishnan. "Linear estimation for the extended exponential power distribution." Journal of Statistical Computation and Simulation 86, no. 7 (July 13, 2015): 1392–403. http://dx.doi.org/10.1080/00949655.2015.1064927.

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39

Habibi, M., and A. Asgharzadeh. "Power binomial exponential distribution: Modeling, simulation and application." Communications in Statistics - Simulation and Computation 47, no. 10 (October 5, 2017): 3042–61. http://dx.doi.org/10.1080/03610918.2017.1367807.

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40

Ida, T., and H. Hibino. "Symmetrization of diffraction peak profiles measured with a high-resolution synchrotron X-ray powder diffractometer." Journal of Applied Crystallography 39, no. 1 (January 12, 2006): 90–100. http://dx.doi.org/10.1107/s0021889805040318.

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The asymmetry of diffraction peak profiles observed with a high-resolution synchrotron powder X-ray diffractometer has been successfully removed by a double deconvolution method. In the first step, the asymmetry caused by the axial divergence aberration of the diffractometer is removed by a whole-pattern deconvolution method based on ana prioritheoretical model for the aberration. In the second step, the residual asymmetry, the origin of which can be ascribed to the aberrations of the beamline optics, is also removed by a whole-pattern deconvolution method, based on an empirical model derived from the analysis of experimental diffraction peak profiles of a standard Si powder (NIST SRM640b). The beamline aberration has been modelled by the convolution of a pseudo-Voigt or Voigt function with an exponential distribution function. It has been found that the angular dependence of the asymmetry parameter in the exponential function is almost proportional to tanθ, which supports the idea that the residual asymmetry should be ascribed mainly to the intrinsic asymmetry in the spectroscopic distribution of the source X-ray supplied by the beamline optics of the synchrotron facility. Recently developed procedures of whole-pattern deconvolution have been improved to treat the singularity of the instrumental function in the measured angular range. Formulae for the whole-pattern deconvolution based on the Williamson–Hall-type dependence of the width parameter of the instrumental function have also been developed. The method was applied to the diffraction intensity data of a standard ZnO powder sample (NIST SRM674) measured with a high-resolution powder diffractometer on beamline BL4B2at the Photon Factory. The structure parameters of ZnO were refined from the integrated peak intensities, which were extracted by an individual profile fitting method applying symmetric profile models. The refined structure parameters coincide fairly well with those obtained from single-crystal data.

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Xu, X. M., and M. S. Ridout. "Effects of Quadrat Size and Shape, Initial Epidemic Conditions, and Spore Dispersal Gradient on Spatial Statistics of Plant Disease Epidemics." Phytopathology® 90, no. 7 (July 2000): 738–50. http://dx.doi.org/10.1094/phyto.2000.90.7.738.

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The spatiotemporal spread of plant diseases was simulated using a stochastic model to study the effects of initial conditions (number of plants initially infected and their spatial pattern), spore dispersal gradient, and size and shape of sampling quadrats on statistics describing the spatiotemporal dynamics of epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance μ (units of distance). A total of 54 different quadrat types, including 23 distinct sizes ranging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (α, β) was fitted to the sampled epidemic data using each of the 54 quadrats for each replicate simulation run. The α and β estimates were highly correlated positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (κ) was calculated for each quadrat type; κ decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three parameters (α 1, β1, β2) was used to relate κ to the disease incidence (p); β1 was highly correlated to β: β1 ≈ β - 1. In general, initial conditions and quadrat size affected α, β, α1, β1, and β2 greatly. The parameter estimates increased as quadrat size increased, and the relationships were described well by a linear regression model on the logarithm of quadrat size with the slope or intercept parameters dependent on initial conditions and μ. Compared with initial conditions and quadrat size, the overall effects of μ and quadrat shape were generally small, although within each quadrat size and initial condition they could be substantial. Quadrat shape had the greatest effect when the quadrat was long and thin. The relationship of the index of dispersion (D) to p and quadrat size was determined from the α and β estimates. D was greatest when p was 0.5 and decreased when p approached 0 or 1. It increased with quadrat size and the rate of the increase was maximum when p was 0.5 and decreased when p approached 0 or 1.

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42

Tovar-Falón, Roger, Heleno Bolfarine, and Guillermo Martínez-Flórez. "The Asymmetric Alpha-Power Skew-t Distribution." Symmetry 12, no. 1 (January 2, 2020): 82. http://dx.doi.org/10.3390/sym12010082.

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In this paper, we propose a new asymmetric and heavy-tail model that generalizes both the skew-t and power-t models. Properties of the model are studied in detail. The score functions and the elements of the observed information matrix are given. The process to estimate the parameters in model is discussed by using the maximum likelihood approach. Also, the observed information matrix is shown to be non-singular at the whole parametric space. Two applications to real data sets are reported to demonstrate the usefulness of this new model.

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Singh, Amita, J. René van Dorp, and Thomas A. Mazzuchi. "A Novel Asymmetric Distribution with Power Tails." Communications in Statistics - Theory and Methods 36, no. 2 (February 6, 2007): 235–52. http://dx.doi.org/10.1080/03610920600974567.

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Kumar, Dinesh, Pradip Kumar, Sanjay Kumar Singh, and Umesh Singh. "A New Asymmetric Loss Function: Estimation of Parameter of Exponential Distribution." Journal of Statistics Applications & Probability Letters 6, no. 1 (January 1, 2019): 37–50. http://dx.doi.org/10.18576/jsapl/060105.

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45

Pak, Ro Jin. "Minimum Density Power Divergence Estimation for Normal-Exponential Distribution." Korean Journal of Applied Statistics 27, no. 3 (June 30, 2014): 397–406. http://dx.doi.org/10.5351/kjas.2014.27.3.397.

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Hassan, Amal S., Rokaya E. Mohamd, M. Elgarhy, and Aisha Fayomi. "Alpha power transformed extended exponential distribution: properties and applications." Journal of Nonlinear Sciences and Applications 12, no. 04 (December 5, 2018): 239–51. http://dx.doi.org/10.22436/jnsa.012.04.05.

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Chaudhary, A. K. "Bayesian Analysis of Two Parameter Complementary Exponential Power Distribution." NCC Journal 3, no. 1 (June 14, 2018): 1–23. http://dx.doi.org/10.3126/nccj.v3i1.20244.

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In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of CEP distribution based on a complete sample. A procedure is developed to obtain Bayes estimates of the parameters of the CEP distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. The MCMC methods have been shown to be easier to implement computationally, the estimates always exist and are statistically consistent, and their probability intervals are convenient to construct. The R functions are developed to study the statistical properties, model validation and comparison tools of the distribution and the output analysis of MCMC samples generated from OpenBUGS. A real data set is considered for illustration under uniform and gamma sets of priors. NCC Journal Vol. 3, No. 1, 2018, Page: 1-23

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Elbatal, I., Mohamed Zayed, Mahdi Rasekhi, and Nadeem Shafique Butt. "The Exponential Pareto Power Series Distribution: Theory and Applications." Pakistan Journal of Statistics and Operation Research 13, no. 3 (September 1, 2017): 603. http://dx.doi.org/10.18187/pjsor.v13i3.2072.

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Salinas, Hugo S., Reinaldo B. Arellano-Valle, and Héctor W. Gómez. "The Extended Skew-Exponential Power Distribution and Its Derivation." Communications in Statistics - Theory and Methods 36, no. 9 (July 10, 2007): 1673–89. http://dx.doi.org/10.1080/03610920601126118.

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Taiwo, Soyinka Ajibola, and Olosunde A. Akin. "A Note On Order Statistics from Exponential Power Distribution." International Journal of Algebra and Statistics 6, no. 1-2 (September 19, 2017): 138. http://dx.doi.org/10.20454/ijas.2017.1269.

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In this paper, we derived probability density function (pdf) for the order statistics from eponential power distribution (EPD). The distribution is flexible at the tail region, because of the presence of shape parameter, which regulates the thickness of the tail. The first moment of the obtained distribution of the order statistics from EPD is presented as well as other measures of central tendencies. This results generalized the results on order statistics from the Laplace distribution and also the results obtained by Arnold, Balakrishnan and Nagaraja on order statistics from normal distribution.

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