nach oben

Annals of Data Science

Erschienen in:

13.01.2017

Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution

verfasst von: Yogesh Mani Tripathi, Amulya Kumar Mahto, Sanku Dey

Erschienen in: Annals of Data Science | Ausgabe 1/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The generalized logistic distribution is a useful extension of the logistic distribution, allowing for increasing and bathtub shaped hazard rates and has been used to model the data with a unimodal density. Here, we consider estimation of the probability density function and the cumulative distribution function of the generalized logistic distribution. The following estimators are considered: maximum likelihood estimator, uniformly minimum variance unbiased estimator (UMVUE), least square estimator, weighted least square estimator, percentile estimator, maximum product spacing estimator, Cramér–von-Mises estimator and Anderson–Darling estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies are also carried out to show that the maximum-likelihood estimator is better than the UMVUE and that the UMVUE is better than others. Finally, a real data set has been analyzed for illustrative purposes.

Vorheriger Artikel A New Extension of Weibull Distribution with Application to Lifetime Data

Nächster Artikel A Measure of SCM Bullwhip Effect Under Mixed Autoregressive-Moving Average with Errors Heteroscedasticity (ARMA(1,1)–GARCH(1,1)) Model

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Ahuja JC, Nash SW (1967) The generalized Gompertz-Verhulst family of distributions. Sankhyã: Indian J Stat, Series A (1961–2002) 29(2):141–156

Alizadeh M, Bagheri SF, Baloui Jamkhaneh E, Nadarajah S (2015a) Estimates of the PDF and the CDF of the exponentiated Weibull distribution. Braz J Probab Stat 29:695–716CrossRef

Alizadeh M, Rezaei S, Bagheri SF (2015b) On the estimation for the Weibull distribution. Ann Data Sci. doi:10.1007/s40745-015-0046-8

Alkasasbeh MR, Raqab MZ (2009) Estimation of the generalized logistic distribution parameters: comparative study. Stat Methodol 6:262–279CrossRef

Anderson TW, Darling DA (1952) Asymptotic theory of certain ‘goodness-of-fit’ criteria based on stochastic processes. Ann Math Stat 23:193–212CrossRef

Asrabadi BR (1990) Estimation in the Pareto distribution. Metrika 37:199–205CrossRef

Badar MG, Priest AM (1982) Statistical aspects of fiber and bundle strength in hybrid composites. In: Hayashi T, Kawata K, Umekawa S (eds) Prog Sci Eng Compos. Tokyo, ICCM-IV, pp 1129–1136

Bagheri SF, Alizadeh M, Nadarajah S (2016) Efficient estimation of the PDF and the CDF of the exponentiated Gumbel distribution. J Commun Stat Simul Comput 45:339–361CrossRef

Bagheri SF, Alizadeh M, Nadarajah S, Deiri E (2014) Efficient estimation of the PDF and the CDF of the Weibull extension model. J Commun Stat Simul Comput. doi:10.1080/03610918.2014.894059

10.

Balakrishnan N, Leung MY (1988) Means, variances and covariances of order statistics, BLUE’s for the Type-I generalized logistic distribution, and some applications. J Commun Stat Simul Comput 17:51–84CrossRef

11.

Balakrishnan N (1990) Approximate maximum likelihood estimation for a generalized logistic distribution. J Stat Plan Inference 26:221–236CrossRef

12.

Balakrishnan N (1992) Handbook of the logistic distribution, statistics: textbooks and monographs, vol 123. Marcel Dekker, New York

13.

Balakrishnan N, Lee SK (1998) Order statistics from the Type III generalized logistic distribution and applications. In: Balakrishnan N, Rao CR (eds) Handbook of statistics, vol 17. North-Holland, Amsterdam, pp 127–155

14.

Bratpvrbajgyran S (2012) A test of goodness of fit for Rayleigh distribution via cumulative residual entropy. In: Proceedings of the 8th world congress in probability and statistics

15.

Cheng RCH and Amin NAK (1979) Maximum product of spacings estimation with application to the lognormal distribution. University of Wales Institute of Science and Technology, Cardiff, Math. Report 79-1

16.

Cheng RCH, Amin NAK (1983) Estimating parameters in continuous univariate distributions with a shifted origin. J R Stat Soc Ser B 45:394–403

17.

Dattner I, Reiser B (2013) Estimation of distribution functions in measurement error models. J Stat Plan Inference 143:479–493CrossRef

18.

Dixit UJ, Jabbari Nooghabi M (2010) Efficient estimation in the Pareto distribution. Stat Methodol 7:687–691CrossRef

19.

Dixit UJ, Jabbari Nooghabi M (2011) Efficient estimation in the Pareto distribution with the presence of outliers. Stat Methodol 8:340–355CrossRef

20.

Durot C, Huet S, Koladjo F, Robin S (2013) Least-squares estimation of a convex discrete distribution. Comput Stat Data Anal 67:282–298CrossRef

21.

Duval C (2013) Density estimation for compound Poisson processes from discrete data. Stoch Process Their Appl 123:3963–3986CrossRef

22.

Er GK (1998) A method for multi-parameter PDF estimation of random variables. Struct Saf 20:25–36CrossRef

23.

Gastwirth JL (1972) The estimation of the Lorenz curve and Gini index. Rev Econ Stat 54:306316CrossRef

24.

Hampel D (2008) Estimation of differential entropy for positive random variables and its application in computational neuroscience. In: Bellomo N (ed) Modeling and simulation in science. engineering and technology, vol 2. Birkhuser, Boston, p 213224

25.

Hartley HO (1945) Note on the calculation of the distribution of the estimate of mean deviation in normal samples. Biometrika 33:257258CrossRef

26.

Hsieh HK (1990) Estimating the critical time of the inverse Gaussian hazard rate. IEEE Trans Reliab 39:342345CrossRef

27.

Hurvich CM, Shumway R, Tsai CL (1990) Improved estimators of Kullback–Leibler information for autoregressive model selection in small samples. Biometrika 77:709719

28.

Jabbari Nooghabi M, Jabbari Nooghabi H (2010) Efficient estimation of PDF, CDF and rth moment for the exponentiated Pareto distribution in the presence of outliers. Statistics 44:1–20CrossRef

29.

Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distribution, vol 1, 2nd edn. Wiley, New York

30.

Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, vol 2, 2nd edn. Wiley, New York

31.

Kao JHK (1958) Computer methods for estimating Weibull parameters in reliability studies. Trans IRE-Reliab Qual Control 13:15–22CrossRef

32.

Kao JHK (1959) A graphical estimation of mixed Weibull parameters in life testing electron tubes. Technometrics 1:389–407CrossRef

33.

Kayal S, Kumar S, Vellaisamy P (2013) Estimating the Rnyi entropy of several exponential populations. Braz J Probab Stat 29(1):94111

34.

Lin CT, Wu SJS, Balakrishnan N (2003) Parameter estimation for the linear hazard rate distribution based on records and inter-record times. Commun Stat-Theory Methods 32:729–748CrossRef

35.

Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New York

36.

Mielniczuk J, Wojtys M (2010) Estimation of Fisher information using model selection. Metrika 72:163187CrossRef

37.

Nilsson M, Kleijn WB (2007) On the estimation of differential entropy from data located on embedded manifolds. IEEE Trans Inf Theory 53:2330–2341CrossRef

38.

Olapade AK (2004) On extended Type-I generalized logistic distribution. Int J Math Math Sci 57:3069–3074CrossRef

39.

Przybilla C, Fernandez-Canteli A, Castillo E (2013) Maximum likelihood estimation for the three-parameter Weibull cdf of strength in presence of concurrent flaw populations. J Eur Ceram Soc 33:1721–1727CrossRef

40.

Saleh Ehsanes Md AK, Hassanein KM, Masoom Ali M (1988) Estimation and testing of hypotheses about the quantile function of the normal distribution. J Inf Optim Sci 9:8598

41.

Saunders SC, Myhre JM (1983) Maximum likelihood estimation for two-parameter decreasing hazard rate distributions using censored data. J Am Stat Assoc 78:664–673CrossRef

42.

Suzuki G (1965) A consistent estimator for the mean deviation of the Pearson type distribution. Ann Inst Stat Math 17:271–285CrossRef

43.

Swain J, Venkatraman S, Wilson J (1988) Least squares estimation of distribution function in Johnson’s translation system. J Stat Comput Simul 29:71–297CrossRef

44.

Wang QJ (1990) Unbiased estimation of probability weighted moments and partial probability weighted moments from systematic and historical flood information and their application to estimating the GEV distribution. J Hydrol 120:115–124CrossRef

45.

Woo JS, Yoon GE (2001) Estimations of Lorenz curve and Gini index in a Pareto distribution. Commun Stat Appl Methods 8:249–256

Titel: Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution
verfasst von: Yogesh Mani Tripathi
Amulya Kumar Mahto
Sanku Dey
Publikationsdatum: 13.01.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Annals of Data Science / Ausgabe 1/2017
Print ISSN: 2198-5804
Elektronische ISSN: 2198-5812
DOI: https://doi.org/10.1007/s40745-016-0093-9

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 1/2017

Big Data Paradigm: What is the Status of Privacy and Security?

A Data-Driven Dynamic Programming Model for Research Position Demand Forecasting

A Measure of SCM Bullwhip Effect Under Mixed Autoregressive-Moving Average with Errors Heteroscedasticity (ARMA(1,1)–GARCH(1,1)) Model

Phylogenetic Trees Construction with Compressed DNA Sequences Using GENBIT COMPRESS Tool

Convex Shape Preservation of Cubic Spline Fits

A New Extension of Weibull Distribution with Application to Lifetime Data