View More View Less
  • 1 Universidade Federal de Pernambuco, Recife/PE, Brazil
  • 2 Universidade Federal do Rio Grande do Norte, Natal/RN, Brazil
  • 3 Universidade Federal de Pernambuco, Recife/PE, Brazil
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

We propose a new two-parameter continuous model called the extended arcsine distribution restricted to the unit interval. It is a very competitive model to the beta and Kumaraswamy distributions for modeling percentages, rates, fractions and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating and quantile functions, Shannon entropy and order statistics. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. We demonstrate by means of two applications to proportional data that it can give consistently a better fit than other important statistical models.

  • [1]

    Alexander, C., Cordeiro, G .M., Ortega, E. M. M. and Sarabia, J. M., Generalized beta-generated distributions, Computational Statistics and Data Analysis, 56 (2012), 18801897.

    • Search Google Scholar
    • Export Citation
  • [2]

    Balakrishnan, N. and Nevzorov, V. B., A Primer on Statistical Distributions, John Wiley & Sons, New Jersey (2003).

  • [3]

    Burnham, K. P. and Anderson, D. R., Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer, New York (2002).

    • Search Google Scholar
    • Export Citation
  • [4]

    Carrasco, J. M. F. , Ortega, E. M. M. and Cordeiro, G. M., A generalized modified Weibull distribution for lifetime modeling, Computational Statistics and Data Analysis, 53 (2008), 450462.

    • Search Google Scholar
    • Export Citation
  • [5]

    Chaudhry, M. A. and Zubair, S. M., On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall/CRC, London (2002).

  • [6]

    Cordeiro, G. M. and de Castro, M., A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81 (2011), 883898.

    • Search Google Scholar
    • Export Citation
  • [7]

    Cordeiro, G. M., Ortega, E. M. M. and Cunha, D. C. C., The exponentiated generalized class of distributions, Journal of Data Science, 11 (2013), 127.

    • Search Google Scholar
    • Export Citation
  • [8]

    Doornik, J. A., An Object-Oriented Matrix Language–Ox 6, Timberlake Consultants Press, London (2009).

  • [9]

    Eugene, N. , Lee, C. and Famoye, F., Beta-normal distribution and its applications. Communications in Statistics –Theory and Methods, 31 (2002), 497512.

    • Search Google Scholar
    • Export Citation
  • [10]

    Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, Academic Press, New York (2007).

  • [11]

    Gupta, R. C. and Kundu, D., Exponentiated exponential distribution: An alternative to gamma and Weibull distributions, Biometrical Journal, 43 (2001), 117130.

    • Search Google Scholar
    • Export Citation
  • [12]

    Gusmao, F. R. S., Ortega, E. M. M. and Cordeiro, G. M., The generalized inverse Weibull distribution, Statistical Papers, 52 (2011), 591619.

    • Search Google Scholar
    • Export Citation
  • [13]

    Jiang, R. and Murthy, D. N. P., The exponentiated Weibull family: a graphical approach, IEEE Transactionson Reliability, 48 (1999), 6872.

    • Search Google Scholar
    • Export Citation
  • [14]

    Kenney, J. F. and Keeping, E. S., Mathematics of Statistics, pp. 101102, Part 1, 3rd ed. Princeton, NJ(1962).

  • [15]

    Kumaraswamy, P., Generalized probability density-function for double-bounded random-processes, Journal of Hydrology, 46 (1980), 7988.

    • Search Google Scholar
    • Export Citation
  • [16]

    Lee, C., Famoye, F. and Alzaatreh, A. Y., Methods for generating families of univariate continuous distributions in the recent decades, WIREs Computational Statistics, 5 (2013), 219238.

    • Search Google Scholar
    • Export Citation
  • [17]

    Lemonte, A. J., Barreto-Souza, W. and Cordeiro, G. M., The exponentiated Kumaraswamy distribution and its log-transform, Brazilian Journal of Probability and Statistics, 27 (2013), 3153.

    • Search Google Scholar
    • Export Citation
  • [18]

    Lemonte, A. J. and Cordeiro, G. M., The exponentiated generalized inverse Gaussian distribution, Statistics and Probability Letters, 81 (2011), 506517.

    • Search Google Scholar
    • Export Citation
  • [19]

    McDonald, J. B. , Some generalized functions for the size distribution of income. Econometrica, 52 (1984), 647663.

  • [20]

    Moors, J. J. A. , A quantile alternative for kurtosis, Journal of the Royal Statistical Society D, 37 (1998), 2532.

  • [21]

    Mudholkar, G. S. and Hutson, A. D., The exponentiated Weibull family: Some properties and a flood data application, Communications in Statistics –Theory and Methods, 25 (1996), 30593083.

    • Search Google Scholar
    • Export Citation
  • [22]

    Mudholkar, G. S., Srivastava, D. K. and Freimer, M., The exponentiated Weibull family, Technometrics, 37 (1995), 436445.

  • [23]

    Nadarajah, S., Cordeiro, G. M. and Ortega, E. M. M., The exponentiated Weibull distribution: a survey, Statistical Papers, 54 (2013), 839877.

    • Search Google Scholar
    • Export Citation
  • [24]

    Nadarajah, S. and Gupta, A. K., The exponentiated gamma distribution with application to drought data, Calcutta Statistical Association Bulletin, 59 (2007), 2954.

    • Search Google Scholar
    • Export Citation
  • [25]

    Ristić, M. M. and Balakrishnan, N., The gamma-exponentiated exponential distribution, Journal of Statistical Computation and Simulation, 82 (2012), 11911206.

    • Search Google Scholar
    • Export Citation
  • [26]

    Zografos, K. and Balakrishnan, N., On families of beta-and generalized gammagenerated distribution and associate inference, Statistical Methodology, 6 (2009), 344362.

    • Search Google Scholar
    • Export Citation

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE

 

  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu