Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
Extended Lindley Distribution with Applications
Distribución Lindley transmutada de rango cúbico con aplicaciones
DOI:
https://doi.org/10.15446/rce.v45n1.93548Palabras clave:
Lindley Distribution, Cubic Rank Transmutation Map, Reliability Analysis, Parameter Estimation (en)Análisis de foabilidad, Distribución Lindley, Estimación de parámetros, Mapa de transmutación de rango cúbico (es)
Descargas
In this work, we propose a three-parameter generalized Lindley distribution using the cubic rank transmutation map approach by Granzotto, Louzada & Balakrishnan (2017). We derive expressions for several mathematical properties including moments and moment generating function, mean deviation, probability weighted moments, quantile function, reliability analysis, and order statistics. We conducted a simulation study to assess the performance of the maximum likelihood estimation procedure for estimating model parameters. The flexibility of the proposed model is illustrated by analyzing two real data sets.
En este trabajo, proponemos una distribución generalizada Lindley con tres parámetros utilizando el enfoque de mapa de transmutación de rango cúbico de Granzotto et al. (2017). Derivamos expresiones para varias propiedades matemáticas, incluyendo momentos y función generadora de momentos, desviación media, momentos ponderados por probabilidad, función cuantil, análisis de conabilidad y estadísticas de orden. Se realizó un estudio de simulación para evaluar el rendimiento del procedimiento de estimación de máxima verosimilitud para estimar los parámetros del modelo. La exibilidad del modelo propuesto se ilustra mediante el análisis de dos conjuntos de datos reales.
Referencias
Alizadeh, M., Merovci, F. & Hamedani, G. G. (2017), ‘Generalized transmuted family of distributions: properties and applications’, Hacettepe Journal of Mathematics and Statistics 46(4), 645– 667. DOI: https://doi.org/10.15672/HJMS.201610915478
Ascher, H. & Feingold, H. (1984), Repairable Systems Reliability Modelling, Inference, Misconceptions and Their Causes, Marcel Dekker, New York.
Asgharzadeh, A., Nadarajah, S. & Sharafi, F. (2018), ‘Weibull Lindley distribution’, REVSTAT Statistical Journal 16(1), 87–113.
Ball, C., Rimal, B. & Chhetri, S. (2021), ‘A New Generalized Cauchy Distribution with an Application to Annual One Day Maximum Rainfall Data’, Statistics, Optimization & Information Computing 9(1), 123–136. DOI: https://doi.org/10.19139/soic-2310-5070-1000
Bhatti, F., Hamedani, G. G., Najibi, S. N. & Ahmad, M. (2020), ‘Cubic Rank Transmuted Modified Burr III Distribution: Development, Properties, Characterizations and Application’, Journal of Data Science 18(2), 299–318. DOI: https://doi.org/10.6339/JDS.202004_18(2).0005
Bjerkedal, T. (1960), ‘Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli’, American Journal of Hygiene pp. 130–148. DOI: https://doi.org/10.1093/oxfordjournals.aje.a120129
Celik, N. (2018), ‘Some cubic rank transmuted distributions’, Journal of Applied Mathematics, Statistics and Informatics 14(2), 27–43. DOI: https://doi.org/10.2478/jamsi-2018-0011
Chhetri, S. B., Akinsete, A. A., Aryal, G. & Long, H. (2017), ‘The Kumaraswamy transmuted Pareto distribution’, Journal of Statistical Distributions and Applications 4(11). DOI: https://doi.org/10.1186/s40488-017-0065-4
Chhetri, S. B., Long, H. & Aryal, G. (2017), ‘The Beta Transmuted Pareto Distribution: Theory and Applications’, Journal of Statistics Applications & Probability 6(2), 243–258. DOI: https://doi.org/10.18576/jsap/060201
Deshpande, J. V., Mukhopadhyay, M. & Naik Nimbalkar, U. V. (2000), ‘Bayesian Nonparametric Estimation of Intensity Functions using Markov Chain Monte Carlo Method’, Calcutta Statistical Association Bulletin 50(3-4), 223–235. DOI: https://doi.org/10.1177/0008068320000309
Ghitany, M. E., Alqallaf, F., Al-Mutairi, D. K. & Husain, H. A. (2011), ‘A twoparameter weighted Lindley distribution and its applications to survival data’, Mathematics and Computers in Simulation 81(6), 1190–1201. DOI: https://doi.org/10.1016/j.matcom.2010.11.005
Ghitany, M. E., Atieh, B. & Nadarajah, S. (2008), ‘Lindley distribution and its Application’, Mathematics Computing and Simulation 78(4), 493–506. DOI: https://doi.org/10.1016/j.matcom.2007.06.007
Gilchrist, W. G. (2000), Statistical Modelling with Quantile Functions, Chapman & Hall/CRC. DOI: https://doi.org/10.1201/9781420035919
Granzotto, D. C. T., Louzada, F. & Balakrishnan, N. (2017), ‘Cubic rank transmuted distributions: inferential issues and applications’, Journal of Statistical Computation and Simulation 87(14), 2760–2778. DOI: https://doi.org/10.1080/00949655.2017.1344239
Greenwood, J. A., Landwehr, J. M., Matalas, N. C. & Wallis, J. R. (1979), ‘Probability weighted moments: Definition and relation to parameters of several distributions expressible in inverse form’, Water Resources Research 15(5), 1049–1054. DOI: https://doi.org/10.1029/WR015i005p01049
Ieren, T. G. & Abdullahi, J. (2020), ‘A Transmuted Normal Distribution: Properties and Applications’, Equity Journal of Science and Technology 7(1), 16–35.
Khan, M. S., King, R. & Hudson, I. L. (2014), ‘Characterisations of the transmuted inverse Weibull distribution’, ANZIAM Journal 55, C197–C217. DOI: https://doi.org/10.21914/anziamj.v55i0.7785
Khokhar, J., Khalil, R. & Shahid, N. (2020), ‘Zografos Balakrishnan Power Lindley Distriution’, Journal of Data Science 18(2), 279–298. DOI: https://doi.org/10.6339/JDS.202004_18(2).0004
Kumar, C. S. & Jose, R. (2018), ‘On double Lindley distribution and some of its properties’, American Journal of Mathematical and Management Sciences 38(1), 23–43. DOI: https://doi.org/10.1080/01966324.2018.1480437
Lindley, D. V. (1958), ‘Fiducial Distributions and Bayes’ Theorem’, Journal of the Royal Statistical Society. Series B (Methodological) 20(1), 102–107. DOI: https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
Meeker, W. Q. & Escobar, L. A. (1998), Statistical Methods for Reliability Data, John Wiley & Sons.
Merovci, F. & Sharma, V. K. (2014), ‘The Beta- Lindley Distribution: Properties and Applications’, Mathematics and Computers in Simulation 2014. DOI: https://doi.org/10.1155/2014/198951
Nadarajah, S., Bakouch, H. S. & Tahmasbi, R. (2011), ‘A generalized Lindley distribution’, Sankhya 73, 331–359. DOI: https://doi.org/10.1007/s13571-011-0025-9
Nofal, Z., Afify, A., Yousof, H. & Cordeiro, G. (2017), ‘The generalized transmuted-g family of distributions’, Communications in Statistics-Theory and Methods 46(8), 41194136. DOI: https://doi.org/10.1080/03610926.2015.1078478
Pararai, M., Warahena-Liyanage, G. & Oluyede, B. O. (2015), ‘Extended Lindley Poisson distribution’, Journal of Mathematics and Statistical Science 1(5), 167–198.
Pekalp, H., Aydogdu, H. & Karabulut, I. (2014), ‘Investigation of trend by graphical methods in counting processes’, Communications Faculty of Science University of Ankara Series A1 Mathematics and Statistics 63(1), 73–83. DOI: https://doi.org/10.1501/Commua1_0000000706
R Core Team (2020), ‘R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria’. https://www.Rproject.org/
Riffi, M. I. (2019), ‘Higher Rank Transmuted Families of Distributions’, IUG Journal of Natural Studies Peer-reviewed Journal of Islamic University-Gaza 27(2), 50–62.
Sankaran, M. (1970), ‘275 note: The discrete Poisson- Lindley distribution’, Biometrics 26(1), 145–149. DOI: https://doi.org/10.2307/2529053
Shanker, R., Fesshaye, H. & Selvaraj, S. (2016), ‘On Modeling of Lifetime Data Using Akash, Shanker, Lindley and Exponential Distributions’, Biometrics and Biostatistics International Journal 3(6), 56–62. DOI: https://doi.org/10.15406/bbij.2016.03.00084
Shanker, R., Sharma, S. & Shanker, R. (2013), ‘A two-parameter Lindley distribution for modeling waiting and survival times data’, Applied Mathematics 4(2), 363–368. DOI: https://doi.org/10.4236/am.2013.42056
Shaw, W. & Buckley, I. (2007), ‘The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map’, Research report pp. 2760–2778.
Shaw, W. & Buckley, I. (2009), ‘The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map’, Conference on Computational Finance, IMA, 09010434, Research report .
Zaninetti, L. (2019), ‘The truncated Lindley distribution with applications in astrophysics’, Galaxies 7(2). DOI: https://doi.org/10.3390/galaxies7020061
Cómo citar
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Descargar cita
CrossRef Cited-by
1. Guillermo Martínez-Flórez, Barry C. Arnold, Héctor W. Gómez. (2024). A Bivariate Power Lindley Survival Distribution. Mathematics, 12(21), p.3334. https://doi.org/10.3390/math12213334.
Dimensions
PlumX
- Citations
- Scopus - Citation Indexes: 4
- Captures
- Mendeley - Readers: 1
Visitas a la página del resumen del artículo
Descargas
Licencia
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
- Los autores/as conservarán sus derechos de autor y garantizarán a la revista el derecho de primera publicación de su obra, el cuál estará simultáneamente sujeto a la Licencia de reconocimiento de Creative Commons (CC Atribución 4.0) que permite a terceros compartir la obra siempre que se indique su autor y su primera publicación esta revista.
- Los autores/as podrán adoptar otros acuerdos de licencia no exclusiva de distribución de la versión de la obra publicada (p. ej.: depositarla en un archivo telemático institucional o publicarla en un volumen monográfico) siempre que se indique la publicación inicial en esta revista.
- Se permite y recomienda a los autores/as difundir su obra a través de Internet (p. ej.: en archivos telemáticos institucionales o en su página web) antes y durante el proceso de envío, lo cual puede producir intercambios interesantes y aumentar las citas de la obra publicada. (Véase El efecto del acceso abierto).
