Modified Maximum Likelihood Estimation: Inverse Half Logistic Distribution

R. Subba Rao*, Pushpa Latha Mamidi**, R. R. L. Kantam***
* Professor, Department of Mathematics, SRKR Engineering College, Bhimavaram, Andhra Pradesh, India.
** Assistant Professor, Department of Mathematics, Vishnu Institute of Technology, Bhimavaram, Andhra Pradesh, India.
*** Retired Professor, Department of Statistics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur, Andhra Pradesh, India.
Periodicity:October - December'2016
DOI : https://doi.org/10.26634/jmat.5.4.8306

Abstract

If a random variable follows a particular distribution, then the distribution of the inverse of that random variable is called inverted distribution. In this paper, the pdf of Inverse Half Logistic Distribution (IHLD) is derived. The mathematical properties of this distribution have been studied. The parameter is estimated from a complete sample using the classical maximum likelihood method. The estimating equations are modified to get simpler and efficient estimators. Two methods of modification are suggested. The sampling characteristics of the modified estimates are also presented for performance comparisons.

Keywords

MLE, Ordered Statistics, Taylors Expansion, Asymptotic Variance.

How to Cite this Article?

Rao, R.S., Mamidi, P.L., and Kantam, R.R.L. (2016). Modified Maximum Likelihood Estimation: Inverse Half Logistic Distribution. i-manager’s Journal on Mathematics, 5(4), 11-19. https://doi.org/10.26634/jmat.5.4.8306

References

[1]. Tiku, M.L., (1967). “Estimating the Mean and Standard deviation from a Censored Normal Sample”. Biometrica, Vol.54, pp.155-165.
[2]. Mehrotra, K.G., and Nanda, P., (1974). “Unbiased Estimation of Parameters by Order Statistics in the case of Censored samples”. Biometrika, Vol.61, pp.601-606.
[3]. Pearson, E.S., and Rootzen, H. (1977). “Simple and Highly Efficient Estimators for a Type-I Censored Normal Sample”. Biometrika, Vol.64, No.1, pp.123-128.
[4]. Rosaiah, K., Kantam, R.R.L., and Narasimham, V.L., (1993). “ML and Modified ML Estimation in Gamma Distribution with a known Prior Relation among the parameters”. Pakistan Journal of Statistics, Vol.9, No.3B, pp.37-48.
[5]. Kantam, R.R.L., and Sriram, B., (2001). “Variable control charts based on Gamma distribution”. IAPQR Transactions, Vol.26, No.2, pp.63-77.
[6]. Kantam, R.R.L., and Srinivasa Rao, G. (2002). “Log-Logistic Distribution: Modified Maximum Likelihood Estimation”. Gujarat Statistical Review, Vol.29, No.1 & 2, pp.25-36.
[7]. Kantam and Sriram, (2003). “Maximum Likelihood Estimation from Censored Samples – Some Modifications in Length Biased version of Exponential Model”. Statistical Methods, Vol.5, No.1, pp.63-78.
[8]. K. Rosaiah, and R.R.L. Kantam, (2005). “Acceptance Sampling based on the Inverse Rayleigh Distribution”. Economic Quality Control, Vol.20, No.2, pp.277-286.
[9]. Kersey, and Jing Xiong, (2010). Weighted Inverse Weibull and Beta-Inverse Weibull Distribution (Doctoral Dissertations). Retrieved from Digital Commons - Georgia Southern, 661.
[10]. R. Subba Rao, and R.R.L. Kantam, (2010). “Pareto Distribution- some methods of Estimation”. International Journal of Computational Mathematical Ideas, Vol.2, No.1 & 2.
[11]. Gyan Prakash, (2011). “Bayes Shrinkage Minimax Estimation in Inverse Gaussian distribution”. Applied Mathematics, No.2, pp.830-835.
[12]. B. Srinivasa Rao, J. Pratapa Reddy, and K. Rosaiah, (2012a). “Extreme value charts and ANOM based on Inverse Rayleigh Distribution”. Pakistan Journal of Statistics and Operation Research, Vol.8, No.4, pp.759-766 .
[13]. G. Srinivasa Rao, R.R.L. Kantam, K. Rosaiah, and J. Pratapa Reddy, (2012b). “Acceptance Sampling Plans for percentiles based on the Inverse Rayleigh Distribution”. Electron. J. App. Stat. Anal., Vol.5, No.2, pp.164-177.
[14]. Muhammad Qaiser Shahbaz, Saman Shahbaz, and Nadeem Shafique Butt, (2012). “The Kumaraswamy-Invere Weibull Distribution”. Pak. J. Stat. Oper. Res. Vol.8, No.3, pp.479-489.
[15]. B.Vara Prasad Rao, K.Gangadhara Rao, and B. Srinivasa Rao, (2013). “Inverse Rayleigh Software Reliability Growth Model”. International Journal of Computer Applications, Vol.75, No.6, pp.0975-8887.
[16]. B.Srinivasa Rao, R.R.L.Kantam, and J. Pratapa Reddy, (2013). “Variable Control Charts based on Inverse Rayleigh Distribution”. Journal of Applied Probability and Statistics, Vol.8, No.1, pp.46-57.
[17]. Farhad Yahgmaei, Manoochehr Babanezhad, and Omid S. Moghadam, (2013). “Bayesian Estimation of the Scale Parameter of Inverse Weibull Distribution under the Asymmetric Loss Functions”. Journal of Probability and Statistics, Vol.2013.
[18]. Jeremias Leao, Helton Saulo, Marcelo Bourguignon, Rematp Cintra, Leandro Rego, and Gauss Cordeiro, (2013). “On some properties of the Beta Inverse Rayleigh Distribution”. Chilean Journal of Statistics, Vol.4, No.2, pp.111-131.
[19]. Kantam, R.R.L., Priya, Ch., M., and Ravi Kumar, M.S., (2013). “Modified Maximum Likelihood Estimation in Linear Failure Rate Distribuiton”. InterStat: Statistics on the Internet, Vol.7, No.6.
[20]. Kanchan Jain, Neetu Singla, and Suresh Kumar Sharma, (2014). “The Generalized Inverse Generalized Weibull Distribution and Its Properties”. Journal of Probability, Vol.2014.
[21]. Kusum Lata Singh and R.S. Srivastava, (2014). “Inverse Maxwell Distribution as a Survival Model, Genesis and Parameter Estimation”. Research Journal of Mathematical and Statistical Sciences, Vol.2, No.7, pp.23-28.
[22]. Muhammad Shuaib Khan, (2014). “Modified Inverse Rayleigh Distribution”. International Journal of Computer Applications, Vol. 87, No.13, pp.0975-8887.
[23]. Pawan Kumar Srivastava, and R.S. Srivastava, (2014). “Two Parameter Inverse Chen Distribution as Survival Model”. International Journal of Statistika and Mathematika, Vol.11.
[24]. Reza Azimi and Faramarz Azimi Sarikhanbaglu, (2014). “Bayesian Estimation for the Kumaraswamy-inverse Rayleigh distributon based on progressive first failure censored samples”. International Journal of Scientific World, Vol.2, No.2, pp.42- 47.
[25]. Elbatal, Hiba Z, and Muhammed, (2014). “Exponentiated Generalised Inverse Weibull distribution”. Applied Mathematical Sciences, Vol.8, No.81, pp.3997-4012.
[26]. Ibrahim Elbatal, Francesca Condino, and Filippo Domma, (2014). “Reflected Generalized Beta Inverse Weibull Distribution: definition and properties”. arXiv: 1309.6108 [math.ST].
[27]. R. Subba Rao, R.R.L. Kantam, and G. Prasad, (2015). “Modified Maximum likelihood Estimation in Pareto-Rayleigh distribution”. Golden Research Thoughts, pp.140-152.
[28]. Taras Bodnar, Stepan Mazur, and Krzysztof Podgorski, (2015). “Singular Inverse Wishart Distribution with Application to Portfolio Theory”. Mathematical Statistics Stockholm University Research Report 8.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.