IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v8y2017i2d10.1007_s13198-017-0600-1.html
   My bibliography  Save this article

The Singh–Maddala distribution: properties and estimation

Author

Listed:
  • Devendra Kumar

    (Central University of Haryana)

Abstract

The Singh–Maddala distribution is very flexible and most widely used for modeling the income, wage, expenditure and wealth distribution of the country. Several mathematical and statistical properties of this distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean deviation about mean and median, Bonferroni and Lorenz curves and various entropies) are derived. We establish relations for the single and product moments of generalized order statistics from the Singh–Maddala distribution and then we use these results to compute the first four moments and variance of order statistics and record values for sample different sizes for various values of the shape and scale parameters. For this distribution, two characterizing results based on conditional moments of generalized order statistics and recurrence relations for single moments are established. The method of maximum likelihood is adopted for estimating the unknown parameters. For different parameters settings and sample sizes, the various simulation studies are performed and compared to the performance of the Singh–Maddala distribution. An application of the model to a real data set is presented and compared with the fit attained by some other well-known two and three parameters distributions.

Suggested Citation

  • Devendra Kumar, 2017. "The Singh–Maddala distribution: properties and estimation," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1297-1311, November.
    • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-017-0600-1
    DOI: 10.1007/s13198-017-0600-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-017-0600-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13198-017-0600-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    2. Mahesh Chandra & Nozer D. Singpurwalla, 1981. "Relationships Between Some Notions Which are Common to Reliability Theory and Economics," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 113-121, February.
    3. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    4. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    5. Doiron, Denise J & Barrett, Garry F, 1996. "Inequality in Male and Female Earnings: The Role of Hours and Wages," The Review of Economics and Statistics, MIT Press, vol. 78(3), pages 410-420, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Devendra Kumar & Anju Goyal, 2019. "Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(4), pages 707-736, December.
    2. R. Dhanya Nair & E. I. Abdul Sathar, 2024. "Nonparametric estimation of extropy based measures under right censoring," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2374-2382, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fabio Fiorillo & Agnese Sacchi, 2012. "The Political Economy of the Standard Level of Services: The Role of Income Distribution," CESifo Working Paper Series 3696, CESifo.
    2. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
    3. Gustavo Yamada & Juan Francisco Castro, 2007. "Poverty, inequality, and social policies in Peru: As poor as it gets," Working Papers 07-06, Centro de Investigación, Universidad del Pacífico.
    4. Gengsheng Qin & Baoying Yang & Nelly Belinga-Hall, 2013. "Empirical likelihood-based inferences for the Lorenz curve," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 1-21, February.
    5. Kleiber, Christian, 2005. "The Lorenz curve in economics and econometrics," Technical Reports 2005,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Stanislaw Maciej Kot & Piotr Paradowski, 2022. "The Atlas of Inequality Aversion: Theory and Empirical Evidence from the Luxembourg Income Study Database," LIS Working papers 826, LIS Cross-National Data Center in Luxembourg.
    7. Sarabia, Jose Maria & Castillo, Enrique & Slottje, Daniel J., 2002. "Lorenz ordering between McDonald's generalized functions of the income size distribution," Economics Letters, Elsevier, vol. 75(2), pages 265-270, April.
    8. Guanghua Wan, 2012. "Towards Greater Equality in China: The Economic Growth Dividend," Working Papers 2012/33, Maastricht School of Management.
    9. Stéphane Mussard & Françoise Seyte & Michel Terraza, 2006. "La décomposition de l’indicateur de Gini en sous-groupes : une revue de la littérature," Cahiers de recherche 06-11, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    10. Wilfling, Bernd, 1996. "Lorenz ordering of generalized beta-II income distributions," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 381-388.
    11. Duclos, Jean-Yves, 1998. "Social evaluation functions, economic isolation and the Suits index of progressivity," Journal of Public Economics, Elsevier, vol. 69(1), pages 103-121, July.
    12. Tóth, István György, 2003. "Jövedelemegyenlőtlenségek - tényleg növekszenek, vagy csak úgy látjuk? [Inequalities of income: are they or do they just seem to be increasing?]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(3), pages 209-234.
    13. Juan Antonio Duro & Jordi Teixidó-Figueras & Emilio Padilla, 2014. "The causal factors of international inequality in co2 emissions per capita: a regression-based inequality decomposition analysis," Working Papers 2014/20, Institut d'Economia de Barcelona (IEB).
    14. Duclos, J.Y., 1995. "Economic Isolation, Inequality, and the Suits Index of Progressivity," Papers 9510, Laval - Recherche en Politique Economique.
    15. Dickens, Richard & Machin, Stephen & Manning, Alan, 1998. "Estimating the effect of minimum wages on employment from the distribution of wages: A critical view," Labour Economics, Elsevier, vol. 5(2), pages 109-134, June.
    16. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    17. Xiao Fan Liu & Yu-Liang Liu & Xin-Hang Lu & Qi-Xuan Wang & Tong-Xing Wang, 2016. "The Anatomy of the Global Football Player Transfer Network: Club Functionalities versus Network Properties," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-14, June.
    18. Brülhart, Marius & Parchet, Raphaël, 2014. "Alleged tax competition: The mysterious death of bequest taxes in Switzerland," Journal of Public Economics, Elsevier, vol. 111(C), pages 63-78.
    19. Yoram Amiel & Frank Cowell & Liema Davidovitz & Avraham Polovin, 2008. "Preference reversals and the analysis of income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 305-330, February.
    20. Abdullah Fathi & Al-Wageh A. Farghal & Ahmed A. Soliman, 2022. "Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-017-0600-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.