Research Article
BibTex RIS Cite

Year 2020, Volume: 69 Issue: 1, 1 - 22, 30.06.2020

Omid Kharazmi , Shahla Jahangard

https://doi.org/10.31801/cfsuasmas.439069
Cited By: 10

Abstract

References

  • Barlow, Richard E., and Frank Proschan. Statistical theory of reliability and life testing: probability models. Florida State Univ Tallahassee, 1975.
  • Calabria, R., & Pulcini, G. Point estimation under asymmetric loss functions for left-truncated exponential samples. Communications in Statistics-Theory and Methods (1996), 25(3), 585-600.
  • Chen, M. H., & Shao, Q. M. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics (1999), 8(1), 69-92.
  • Carbone, P. P., Kellerhouse, L. E., & Gehan, E. A. Plasmacytic myeloma: A study of the relationship of survival to various clinical manifestations and anomalous protein type in 112 patients. The American journal of medicine (1967), 42(6), 937-948.
  • Dey, S., Zhang, C., Asgharzadeh, A., & Ghorbannezhad, M. Comparisons of Methods of Estimation for the NH Distribution. Annals of Data Science (2017), 4(4), 441-455.
  • Efron, Bradley, and Robert J. Tibshirani. An introduction to the bootstrap. CRC press, 1994.
  • Kumar, D., Dey, S., & Nadarajah, S. Extended exponential distribution based on order statistics. Communications in Statistics-Theory and Methods (2017), 46(18), 9166-9184.
  • Lemonte, A. J. A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Computational Statistics & Data Analysis (2013), 62, 149-170.
  • Meeker, William Q., and Luis A. Escobar. Statistical methods for reliability data. John Wiley & Sons, 2014.
  • Nadarajah, S., & Haghighi, F. An extension of the exponential distribution. Statistics (2011), 45(6), 543-558.
  • Ramos, M. W. A., Marinho, P. R. D., da Silva, R. V., & Cordeiro, G. M. The exponentiated Lomax Poisson distribution with an application to lifetime data. Advances and Applications in Statistics (2013), 34(2), 107-135.
  • Shaked, Moshe, and J. George Shanthikumar. Stochastic orders. Springer Science & Business Media, 2007.

A new family of lifetime distributions in terms of cumulative hazard rate function

Year 2020, Volume: 69 Issue: 1, 1 - 22, 30.06.2020

Omid Kharazmi , Shahla Jahangard

https://doi.org/10.31801/cfsuasmas.439069
Cited By: 10

Abstract

In the present paper, a new family of lifetime distributions is introduced according to cumulative hazard rate function, the well-known concept in survival analysis and reliability engineering. Some important properties of proposed model including  survival function, quantile function, hazard function, order statistic and some results of stochastic ordering are obtained in  general setting. An especial case of this new family is introduced  by considering Weibull distribution as the parent distribution; in addition estimating unknown parameters of specialized model will be examined from the perspective of Bayesian  and classic statistics.
Moreover, three examples of real data sets: complete, right-censored and progressively type-I interval-censored data are studied; point and interval estimations of all parameters are obtained. Finally, the superiority of proposed model in terms of parent Weibull distribution over other fundamental statistical distributions  is shown via complete real observations.

Keywords

Cumulative hazard rate function Bayesian estimation Maximum likelihood estimation progressively type-I interval-censored data

References

  • Barlow, Richard E., and Frank Proschan. Statistical theory of reliability and life testing: probability models. Florida State Univ Tallahassee, 1975.
  • Calabria, R., & Pulcini, G. Point estimation under asymmetric loss functions for left-truncated exponential samples. Communications in Statistics-Theory and Methods (1996), 25(3), 585-600.
  • Chen, M. H., & Shao, Q. M. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics (1999), 8(1), 69-92.
  • Carbone, P. P., Kellerhouse, L. E., & Gehan, E. A. Plasmacytic myeloma: A study of the relationship of survival to various clinical manifestations and anomalous protein type in 112 patients. The American journal of medicine (1967), 42(6), 937-948.
  • Dey, S., Zhang, C., Asgharzadeh, A., & Ghorbannezhad, M. Comparisons of Methods of Estimation for the NH Distribution. Annals of Data Science (2017), 4(4), 441-455.
  • Efron, Bradley, and Robert J. Tibshirani. An introduction to the bootstrap. CRC press, 1994.
  • Kumar, D., Dey, S., & Nadarajah, S. Extended exponential distribution based on order statistics. Communications in Statistics-Theory and Methods (2017), 46(18), 9166-9184.
  • Lemonte, A. J. A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Computational Statistics & Data Analysis (2013), 62, 149-170.
  • Meeker, William Q., and Luis A. Escobar. Statistical methods for reliability data. John Wiley & Sons, 2014.
  • Nadarajah, S., & Haghighi, F. An extension of the exponential distribution. Statistics (2011), 45(6), 543-558.
  • Ramos, M. W. A., Marinho, P. R. D., da Silva, R. V., & Cordeiro, G. M. The exponentiated Lomax Poisson distribution with an application to lifetime data. Advances and Applications in Statistics (2013), 34(2), 107-135.
  • Shaked, Moshe, and J. George Shanthikumar. Stochastic orders. Springer Science & Business Media, 2007.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Omid Kharazmi 0000-0001-6557-3852

Shahla Jahangard This is me 0000-0001-8550-7537

Publication Date June 30, 2020
Submission Date June 29, 2018
Acceptance Date July 11, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Kharazmi, O., & Jahangard, S. (2020). A new family of lifetime distributions in terms of cumulative hazard rate function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 1-22. https://doi.org/10.31801/cfsuasmas.439069
AMA Kharazmi O, Jahangard S. A new family of lifetime distributions in terms of cumulative hazard rate function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):1-22. doi:10.31801/cfsuasmas.439069
Chicago Kharazmi, Omid, and Shahla Jahangard. “A New Family of Lifetime Distributions in Terms of Cumulative Hazard Rate Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 1-22. https://doi.org/10.31801/cfsuasmas.439069.
EndNote Kharazmi O, Jahangard S (June 1, 2020) A new family of lifetime distributions in terms of cumulative hazard rate function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 1–22.
IEEE O. Kharazmi and S. Jahangard, “A new family of lifetime distributions in terms of cumulative hazard rate function”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 1–22, 2020, doi: 10.31801/cfsuasmas.439069.
ISNAD Kharazmi, Omid - Jahangard, Shahla. “A New Family of Lifetime Distributions in Terms of Cumulative Hazard Rate Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 1-22. https://doi.org/10.31801/cfsuasmas.439069.
JAMA Kharazmi O, Jahangard S. A new family of lifetime distributions in terms of cumulative hazard rate function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1–22.
MLA Kharazmi, Omid and Shahla Jahangard. “A New Family of Lifetime Distributions in Terms of Cumulative Hazard Rate Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 1-22, doi:10.31801/cfsuasmas.439069.
Vancouver Kharazmi O, Jahangard S. A new family of lifetime distributions in terms of cumulative hazard rate function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):1-22.

Cited By

The Global Entrepreneurship Index (GEI): a critical review
Journal of Global Entrepreneurship Research
https://doi.org/10.1007/s40497-021-00302-0
Application of Neural Network and Time-Domain Feature Extraction Techniques for Determining Volumetric Percentages and the Type of Two Phase Flow Regimes Independent of Scale Layer Thickness
Applied Sciences
https://doi.org/10.3390/app12031336
Extraction of Time-Domain Characteristics and Selection of Effective Features Using Correlation Analysis to Increase the Accuracy of Petroleum Fluid Monitoring Systems
Energies
https://doi.org/10.3390/en15061986
Frequency Domain Feature Extraction Investigation to Increase the Accuracy of an Intelligent Nondestructive System for Volume Fraction and Regime Determination of Gas-Water-Oil Three-Phase Flows
Mathematics
https://doi.org/10.3390/math9172091
Applying Data Mining and Artificial Intelligence Techniques for High Precision Measuring of the Two-Phase Flow’s Characteristics Independent of the Pipe’s Scale Layer
Electronics
https://doi.org/10.3390/electronics11030459
Approximation Process Based on Parametric Generalization of Schurer–Kantorovich Operators and their Bivariate Form
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
https://doi.org/10.1007/s40010-022-00786-9
Investigation of Time-Domain Feature Selection and GMDH Neural Network Application for Determination of Volume Percentages in X-Ray-Based Two-Phase Flow Meters
MAPAN
https://doi.org/10.1007/s12647-022-00578-x
Approximation of functions by a new class of generalized Bernstein–Schurer operators
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
https://doi.org/10.1007/s13398-020-00903-6
https://doi.org/
An Investigation on Spiking Neural Networks Based on the Izhikevich Neuronal Model: Spiking Processing and Hardware Approach
Mathematics
https://doi.org/10.3390/math10040612

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.