Skip to main content
SpringerLink
Log in

On the Alpha Power Transformed Power Inverse Lindley Distribution

  • Research Article
  • Published:
Journal of the Indian Society for Probability and Statistics Aims and scope Submit manuscript

Abstract

In this paper, we introduce a new generalization of the power inverse Lindley distribution referred to as the alpha power transformed power inverse Lindley (APTPIL). The APTPIL model provides a better fit than the power inverse Lindley distribution. It includes the alpha power transformed inverse Lindley, power inverse Lindley and inverse Lindley as special sub models. Various properties of the APTPIL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Important data set is employed to show how the proposed model works in practice.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Alkarni SH (2019) Generalized inverse Lindley power series distributions: modeling and simulation. J Nonlinear Sci Appl 12:799–815

    Article  MathSciNet  Google Scholar 

  • Almalki S, Nadarajah S (2014) Modifications of the Weibull distribution: a review. Reliab Eng Syst Saf 124:32–55

    Article  Google Scholar 

  • Almalki S, Yuan J (2013) A new modified Weibull distribution. Reliability Engineering and System Safety 111:164–170

    Article  Google Scholar 

  • Ashour KS, Eltehiwy AM (2015) Exponentiated power Lindley distribution. J Adv Res 6(6):895–905

    Article  Google Scholar 

  • Bakouch HS, Al-Zahrani BM, Al-Shomrani AA, Marchi VA, Louzada F (2012) An extended Lindley distribution. J Korean Stat Soc 41(1):75–85

    Article  MathSciNet  Google Scholar 

  • Barco K, Mazuchile J, Janeiro V (2017) The inverse power Lindley distribution. Commun Stat Simul Comput 46(8):6308–6323

    Article  MathSciNet  Google Scholar 

  • Bjerkedal T (1960) Acquisition of resistance in guinea pies infected with different doses of virulent tubercle bacilli. Am J Hyg 72(1):130–148

    Google Scholar 

  • Cheng RCH, Amin NAK (1979) Maximum product of spacings estimation with application to the lognormal distributions. Math report 79-1, Department of Mathematics, UWIST, Cardiff

  • Cordeiro GM, Silva RB (2014) The complementary extended Weibull power series class of distributions. Cincia Nat 36:1–13

    Google Scholar 

  • Dey S, Sharma VK, Mesfioui M (2017a) A new extension of Weibull distribution with application to lifetime data. Ann Data Sci 1(4):31–61

    Article  Google Scholar 

  • Dey S, Alzaatreh A, Zhang C, Kumar D (2017b) A new extension of generalized exponential distribution with application to ozone data. Ozone Sci Eng 4(39):273–285

    Article  Google Scholar 

  • Dey S, Ghosh I, Kumar D (2018) Alpha-power transformed Lindley distribution: properties and associated inference with application to earthquake data. Ann Data Sci 6:1–28

    Google Scholar 

  • Dey S, Nassar M, Kumar D (2019) Alpha power transformed inverse Lindley distribution: a distribution with an upside down bathtub-shaped hazard function. J Comput Appl Math 348:130–145

    Article  MathSciNet  Google Scholar 

  • Efron B (1988) Logistic regression, survival analysis, and the Kaplan–Meier curve. J Am Stat Assoc 83:414–425

    Article  MathSciNet  Google Scholar 

  • Erto P, Rapone M (1984) Non-informative and practical Bayesian confidence bounds for reliable life in the Weibull model. Reliab Eng 7:181–191

    Article  Google Scholar 

  • Ghitany ME, Atieh B, Nadarajah S (2008) Lindley distribution and its application. Math Comput Simul 78(4):493–506

    Article  MathSciNet  Google Scholar 

  • Ghitany M, Al-Mutairi D, Balakrishnan N, Al-Enezi L (2013) Power Lindley distribution and associated inference. Comput Stat Data Anal 64:20–33

    Article  MathSciNet  Google Scholar 

  • Glen A (2011) On the inverse gamma as a survival distribution. J Qual Technol 43:158–166

    Article  Google Scholar 

  • Gupta R, Kirmani S (1990) The role of weighted distribution in stochastic modeling. Commun Stat Theory Methods 19:3147–3162

    Article  MathSciNet  Google Scholar 

  • Hassan AS, Mohamd RE, Elgarhy M, Fayomi A (2018) Alpha power transformed extended exponential distribution: properties and applications. J Nonlinear Sci Appl 12:62–67

    Article  MathSciNet  Google Scholar 

  • Hassan AS, Elgarhy M, Mohamd RE, Elrajhi R (2019) Alpha power transformed power Lindley distribution. J Probab Stat 2019:8024769

    Article  MathSciNet  Google Scholar 

  • Langlands A, Pocock S, Kerr G, Gore S (1997) Long-term survival of patients with breast cancer: a study of the curability of the disease. Br Med J 2:1247–1251

    Article  Google Scholar 

  • Lindley DV (1958) Fiducial distributions and Bayes theorem. J R Stat Soc Ser B (Methodol) 20:102–107

    MathSciNet  MATH  Google Scholar 

  • Mahdavi A, Kundu D (2017) A new method for generating distributions with an application to exponential distribution. Commun Stat Theory Methods 13(46):6543–6557

    Article  MathSciNet  Google Scholar 

  • Mead M (2015) Generalized inverse gamma distribution and its applications in reliability communications. Commun Stat Theory Methods 44:1426–1435

    Article  Google Scholar 

  • Morais AL, Barreto-Souza W (2011) A compound class of Weibull and power series distributions. Comput Stat Data Anal 55:14101425

    Article  MathSciNet  Google Scholar 

  • Murthy D, Xie M, Jiang R (2004) Weibull models. Wiley, Hoboken

    MATH  Google Scholar 

  • Nadarajah S, Bakouch HS, Tahmasbi R (2011) A generalized Lindley distribution. Sankhya B 73(2):331–359

    Article  MathSciNet  Google Scholar 

  • Patil GP (2002) Weighted distributions. Encycl Environ 4:2369–2377

    Google Scholar 

  • Shaked M, Shanthikumar JG (1994) Stochastic orders and their applications. Academic Press, New York

    MATH  Google Scholar 

  • Shanker R, Mishra A (2013) A two-parameter Lindley distribution. Stat Transit New Ser 14(1):45–56

    MathSciNet  Google Scholar 

  • Sharma V, Singh S, Singh U (2014) A new upside-down bathtub shaped hazard rate model for survival data analysis. Appl Math Comput 239:242–253

    MathSciNet  MATH  Google Scholar 

  • Sharma VK, Singh SK, Singh U, Agiwal V (2015) The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data. J Ind Prod Eng 32(3):162–173

    Google Scholar 

  • Sharma V, Singh S, Singh U, Merovci F (2016) The generalized inverse Lindley distribution: a new inverse statistical model for the study of upside-down bathtub survival data. Commun Stat Theory Methods 45(19):5709–5729

    Article  Google Scholar 

  • Stainslav A, Grigory A (2005) An alternative to maximum likelihood based on spacings. Econom Theory. https://doi.org/10.1017/S0266466605050255

    Article  MathSciNet  Google Scholar 

  • Zakerzadeh H, Dolati A (2009) Generalized Lindley distribution. J Math Ext 3(2):13–25

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Politics and Economics, Beni Suef University, Beni-Suef, Egypt

    Mahmoud Eltehiwy

Authors
  1. Mahmoud Eltehiwy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahmoud Eltehiwy.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eltehiwy, M. On the Alpha Power Transformed Power Inverse Lindley Distribution. J Indian Soc Probab Stat 21, 201–224 (2020). https://doi.org/10.1007/s41096-020-00074-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41096-020-00074-y

Keywords

Search

Navigation