The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution

Sule Ibrahim; Olalekan Akanji Bello; Awodutire Phillip Oluwatobi; Hammed Olanrewaju Lawal

doi:doi:10.11648/j.ijsd.20200604.12

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The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution

Sule Ibrahim, Olalekan Akanji Bello, Awodutire Phillip Oluwatobi, Hammed Olanrewaju Lawal

Published in International Journal of Statistical Distributions and Applications (Volume 6, Issue 4)

Received: 29 October 2016 Accepted: 3 December 2016 Published: 25 December 2020

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Abstract

Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the r^th minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.

Published in	International Journal of Statistical Distributions and Applications (Volume 6, Issue 4)
DOI	10.11648/j.ijsd.20200604.12
Page(s)	71-74
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Characterizations, Generalization, Hazard Function, Logistic Distribution, Order Statistics, Parameter, Reliability, Survival Function

References

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[2]	Balakrishnan, N. and Kocherlakota, S. (1986). On the moments of order statistics from the doubly truncated logistic distribution, Journal of Statistical Planning and Inference. 13, 117-129.
[3]	Balakrishnan, N. and Saleh, H. M. (2011), Relations for moments of progressively Type II censored order Statistics from Log-logistic Distribution with applications to Inference, Computational Statistics and Data Analysis, 55 (10), pp 2775–2792.
[4]	Begum, A. A. and Parvin, S. (2002), Moments of Order Statistics from Doubly Truncated Burr Distribution, J. Statist. Research, 36 (2), 179-190.
[5]	Birnbaum, A. and Dudman, J. (1963), Logistic Order statistics, Ann. Math. Statist., 34 (2), pp 658– 663.
[6]	David, H. A. (1970), Order Statistics. John Wiley, New York.
[7]	George, E. 0. and Rousseau, C. C. (1987). On the logistic midrange, Annals of the Institute Statistical Mathematics. 39, 627-635.
[8]	Gupta, S. S. and Shah, B. K. (1965), Exact Moments and Percentage Points of the Order Statistics and the Distribution of the Range from the Logistic Distribution, Annals of Mathematical Statistics, 36 (3), pp 907–920.
[9]	Govindarajulu, Z. (1963), On moments of order statistics and quasi-ranges from normalpopulations, Annals of Mathematical Statistics. 34, 633-651.
[10]	Johnson, N. L., Kotz S., Balakrishnan N. (1995), Continuous Univariate Distributions Volume 2. Wiley, New York.
[11]	Mathai, A. M. (2003), Order statistics from a logistic distribution and applications to survival and reliability analysis, IEEE Transactions on Reliability, 52 (2), pp 200–206.
[12]	Mohammad, A., George, P. Y and Contantic, O. (2012), Characterizations of Logistic Distribution through Order Statistics with independent Exponential Shift, Economic Quality Control, 27 (1), pp 85–96.
[13]	Olapade, A. K., Sule, I., Bello, A. O. and Braimah, O. J. (2016), On a Five Parameter Type II Generalized Logistic Distribution, Computing, Information Systems, Development Informatics and Allied Research Journal, 7 (1), pp 49–58.
[14]	Olapade, A. K. (2000), Some properties of the Type I Generalized logistic distribution. Intro. Stat. 2.
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[16]	Shah, B. K. (1966), On the Bivariate Moments of Order Statistics from a Logistic Distribution, The Annals of Mathematical Statistics, 37 (4), 1002-1010.
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[18]	Tarter, M. E. and Clark, V. A. (1980), Correction to “Order Statistics of Logistic Variates”, Annals of Mathematical Statistics, 8 (4), pp-935.
[19]	Tarter, M. E. (1966). Exact moment sand product moments of the order statistics from the truncated logistic distribution, Journal of American Statistical Association, 61, 514-525.
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APA Style

Sule Ibrahim, Olalekan Akanji Bello, Awodutire Phillip Oluwatobi, Hammed Olanrewaju Lawal. (2020). The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution. International Journal of Statistical Distributions and Applications, 6(4), 71-74. https://doi.org/10.11648/j.ijsd.20200604.12

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ACS Style

Sule Ibrahim; Olalekan Akanji Bello; Awodutire Phillip Oluwatobi; Hammed Olanrewaju Lawal. The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution. Int. J. Stat. Distrib. Appl. 2020, 6(4), 71-74. doi: 10.11648/j.ijsd.20200604.12

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AMA Style

Sule Ibrahim, Olalekan Akanji Bello, Awodutire Phillip Oluwatobi, Hammed Olanrewaju Lawal. The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution. Int J Stat Distrib Appl. 2020;6(4):71-74. doi: 10.11648/j.ijsd.20200604.12

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@article{10.11648/j.ijsd.20200604.12,
  author = {Sule Ibrahim and Olalekan Akanji Bello and Awodutire Phillip Oluwatobi and Hammed Olanrewaju Lawal},
  title = {The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {4},
  pages = {71-74},
  doi = {10.11648/j.ijsd.20200604.12},
  url = {https://doi.org/10.11648/j.ijsd.20200604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200604.12},
  abstract = {Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the rth minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.},
 year = {2020}
}

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TY  - JOUR
T1  - The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution
AU  - Sule Ibrahim
AU  - Olalekan Akanji Bello
AU  - Awodutire Phillip Oluwatobi
AU  - Hammed Olanrewaju Lawal
Y1  - 2020/12/25
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200604.12
DO  - 10.11648/j.ijsd.20200604.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 71
EP  - 74
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200604.12
AB  - Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the rth minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.
VL  - 6
IS  - 4
ER  -

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Author Information

Sule Ibrahim

Department of Mathematics and Statistics, Ahmadu Bello University, Zaria, Nigeria
Olalekan Akanji Bello

Department of Mathematics and Statistics, Ahmadu Bello University, Zaria, Nigeria
Awodutire Phillip Oluwatobi

Department of Mathematical Science, University of Africa, Toru Orua, Nigeria
Hammed Olanrewaju Lawal

Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria

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Plain Text BibTeX RIS

APA Style

Sule Ibrahim, Olalekan Akanji Bello, Awodutire Phillip Oluwatobi, Hammed Olanrewaju Lawal. (2020). The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution. International Journal of Statistical Distributions and Applications, 6(4), 71-74. https://doi.org/10.11648/j.ijsd.20200604.12

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ACS Style

Sule Ibrahim; Olalekan Akanji Bello; Awodutire Phillip Oluwatobi; Hammed Olanrewaju Lawal. The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution. Int. J. Stat. Distrib. Appl. 2020, 6(4), 71-74. doi: 10.11648/j.ijsd.20200604.12

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AMA Style

Sule Ibrahim, Olalekan Akanji Bello, Awodutire Phillip Oluwatobi, Hammed Olanrewaju Lawal. The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution. Int J Stat Distrib Appl. 2020;6(4):71-74. doi: 10.11648/j.ijsd.20200604.12

Copy | Download

@article{10.11648/j.ijsd.20200604.12,
  author = {Sule Ibrahim and Olalekan Akanji Bello and Awodutire Phillip Oluwatobi and Hammed Olanrewaju Lawal},
  title = {The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {4},
  pages = {71-74},
  doi = {10.11648/j.ijsd.20200604.12},
  url = {https://doi.org/10.11648/j.ijsd.20200604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200604.12},
  abstract = {Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the rth minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution
AU  - Sule Ibrahim
AU  - Olalekan Akanji Bello
AU  - Awodutire Phillip Oluwatobi
AU  - Hammed Olanrewaju Lawal
Y1  - 2020/12/25
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200604.12
DO  - 10.11648/j.ijsd.20200604.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 71
EP  - 74
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200604.12
AB  - Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the rth minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.
VL  - 6
IS  - 4
ER  -

Copy | Download