Modeling COVID-19 Real Data Set by a New Extension of Haq Distribution
<p>Different plots of the PDF of the PHD using different values of parameters.</p> "> Figure 2
<p>Plots of the <inline-formula><mml:math id="mm63"><mml:semantics><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mi>F</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> of the PHD with various parametric values.</p> "> Figure 3
<p>These figures show the histogram of the fitted PDF (top left), CDF (top right), SF (bottom left) and P-P (bottom right) plots of the COVID-19 dataset.</p> "> Figure 4
<p>TTT plot (left) and fitted HRF (right) of the PHD model for the COVID-19 dataset.</p> "> Figure 5
<p>The log-likelihood function plots for parameters <inline-formula><mml:math id="mm64"><mml:semantics><mml:mi>α</mml:mi></mml:semantics></mml:math></inline-formula> and <inline-formula><mml:math id="mm65"><mml:semantics><mml:mi>β</mml:mi></mml:semantics></mml:math></inline-formula>.</p> ">
Abstract
:1. Introduction
2. Model Formulation
Reliability Functions
3. Statistical Properties
3.1. Mode
3.2. Moments
3.3. Incomplete Moments
3.4. Order Statistics
4. Estimation of PHD Parameters
5. Numerical Simulation
- The PHD estimators’ values show the consistency property.
- All measures in the simulation tables decrease, as the sample size increases, except for the CP.
- is always smaller than .
- The maximum spacing product is the estimation method that is most preferred according to the ranking table.
6. Real Data Analysis
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Alshanbari, H.M.; Abd El-Bagoury, A.A.H.; Gemeay, A.M.; Hafez, E.H.; Eldeeb, A.S. A flexible extension of pareto distribution: Properties and applications. Comput. Intell. Neurosci. 2021, 2021, 9819200. [Google Scholar] [CrossRef] [PubMed]
- Alshanbari, H.M.; Gemeay, A.M.; El-Bagoury, A.A.A.H.; Khosa, S.K.; Hafez, E.H.; Muse, A.H. A novel extension of fréchet distribution: Application on real data and simulation. Alex. Eng. J. 2022, 61, 7917–7938. [Google Scholar] [CrossRef]
- Saber, M.M.; Shishebor, Z.; Raouf, M.M.; Hafez, E.H.; Aldallal, R. Most effective sampling scheme for prediction of stationary stochastic processes. Complexity 2022, 2022, 4997675. [Google Scholar] [CrossRef]
- Ashraf, B.N. Economic impact of government interventions during the COVID-19 pandemic: International evidence from financial markets. J. Behav. Exp. Financ. 2020, 27, 100371. [Google Scholar] [CrossRef] [PubMed]
- Sansa, N.A. The impact of the COVID-19 on the financial markets: Evidence from China and USA. Electron. Res. J. Soc. Sci. Humanit. 2020, 2. [Google Scholar] [CrossRef]
- Zhang, D.; Hu, M.; Ji, Q. Financial markets under the global pandemic of COVID-19. Financ. Res. Lett. 2020, 36, 101528. [Google Scholar] [CrossRef] [PubMed]
- Almetwally, E.M.; Abdo, D.A.; Hafez, E.H.; Jawa, T.M.; Sayed-Ahmed, N.; Almongy, H.M. The new discrete distribution with application to COVID-19 data. Results Phys. 2022, 32, 104987. [Google Scholar] [CrossRef] [PubMed]
- Alsuhabi, H.; Alkhairy, I.; Almetwally, E.M.; Almongy, H.M.; Gemeay, A.M.; Hafez, E.H.; Aldallal, R.A.; Sabry, M. A superior extension for the lomax distribution with application to COVID-19 infections real data. Alex. Eng. J. 2022, 61, 11077–11090. [Google Scholar] [CrossRef]
- Bo, W.; Ahmad, Z.; Alanzi, A.R.; Al-Omari, A.I.; Hafez, E.H.; Abdelwahab, S.F. The current COVID-19 pandemic in china: An overview and corona data analysis. Alex. Eng. J. 2022, 61, 1369–1381. [Google Scholar] [CrossRef]
- Almetwally, E.M.; Alharbi, R.; Alnagar, D.; Hafez, E.H. A new inverted topp-leone distribution: Applications to the COVID-19 mortality rate in two different countries. Axioms 2021, 10, 25. [Google Scholar] [CrossRef]
- Almongy, H.M.; Almetwally, E.M.; Aljohani, H.M.; Alghamdi, A.S.; Hafez, E.H. A new extended rayleigh distribution with applications of COVID-19 data. Results Phys. 2021, 23, 104012. [Google Scholar] [CrossRef] [PubMed]
- Alzeley, O.; Almetwally, E.M.; Gemeay, A.M.; Alshanbari, H.M.; Hafez, E.H.; Abu-Moussa, M.H. Statistical inference under censored data for the new exponential-x fréchet distribution: Simulation and application to leukemia data. Comput. Intell. Neurosci. 2021, 2021, 2167670. [Google Scholar] [CrossRef] [PubMed]
- Benati, I.; Coccia, M. Global analysis of timely COVID-19 vaccinations: Improving governance to reinforce response policies for pandemic crises. Int. J. Health Gov. 2022. ahead-of-print. [Google Scholar]
- Jiménez-Rodríguez, P.; Muñoz-Fernández, G.A.; Rodrigo-Chocano, J.C.; Seoane-Sepúlveda, J.B.; Weber, A. A population structure-sensitive mathematical model assessing the effects of vaccination during the third surge of COVID-19 in italy. J. Math. Anal. Appl. 2022, 514, 125975. [Google Scholar] [CrossRef] [PubMed]
- Malik, A.A.; McFadden, S.M.; Elharake, J.; Omer, S.B. Determinants of COVID-19 vaccine acceptance in the us. EClinicalMedicine 2020, 26, 100495. [Google Scholar] [CrossRef] [PubMed]
- Ahsan-ul Haq, M. Statistical analysis of haq distribution: Estimation and applications. Pak. J. Stat. 2022, 38, 473–490. [Google Scholar]
- Afify, A.Z.; Al-Mofleh, H.; Aljohani, H.M.; Cordeiro, G.M. The marshall–olkin–weibull-h family: Estimation, simulations, and applications to COVID-19 data. J. King Saud Univ.-Sci. 2022, 34, 102115. [Google Scholar] [CrossRef]
n | Est. | Est.Par. | MLE | ADE | CVME | MPSE | OLSE | RTADE | WLSE | LTADE | MSADE | MSALDE |
---|---|---|---|---|---|---|---|---|---|---|---|---|
30 | BIAS | 0.0904 | ||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
70 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
150 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
350 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
n | Est. | Est.Par. | MLE | ADE | CVME | MPSE | OLSE | RTADE | WLSE | LTADE | MSADE | MSALDE |
---|---|---|---|---|---|---|---|---|---|---|---|---|
30 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
70 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
150 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
350 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
n | Est. | Est.Par. | MLE | ADE | CVME | MPSE | OLSE | RTADE | WLSE | LTADE | MSADE | MSALDE |
---|---|---|---|---|---|---|---|---|---|---|---|---|
30 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
70 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
150 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
350 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
n | Est. | Est.Par. | MLE | ADE | CVME | MPSE | OLSE | RTADE | WLSE | LTADE | MSADE | MSALDE |
---|---|---|---|---|---|---|---|---|---|---|---|---|
30 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
70 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
150 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
350 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
n | Est. | Est.Par. | MLE | ADE | CVME | MPSE | OLSE | RTADE | WLSE | LTADE | MSADE | MSALDE |
---|---|---|---|---|---|---|---|---|---|---|---|---|
30 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
70 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
150 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
350 | BIAS | |||||||||||
MSE | ||||||||||||
MRE | ||||||||||||
CIL | ||||||||||||
CP | ||||||||||||
ASAE | ||||||||||||
Parameter | n | MLE | ADE | CVME | MPSE | OLSE | RTADE | WLSE | LTADE | MSADE | MSALDE |
---|---|---|---|---|---|---|---|---|---|---|---|
, | 30 | 1.0 | 4.5 | 3.0 | 2.0 | 6.0 | 8.0 | 4.5 | 7.0 | 9.0 | 10.0 |
70 | 1.0 | 4.0 | 6.0 | 2.0 | 5.0 | 8.0 | 3.0 | 7.0 | 10.0 | 9.0 | |
150 | 2.0 | 3.0 | 7.5 | 1.0 | 5.0 | 9.0 | 4.0 | 6.0 | 10.0 | 7.5 | |
350 | 3.0 | 1.0 | 6.0 | 2.0 | 5.0 | 9.0 | 4.0 | 8.0 | 10.0 | 7.0 | |
, | 30 | 2.0 | 3.0 | 9.0 | 1.0 | 5.5 | 7.0 | 4.0 | 5.5 | 10.0 | 8.0 |
70 | 1.0 | 3.0 | 9.0 | 2.0 | 6.0 | 5.0 | 4.0 | 7.0 | 10.0 | 8.0 | |
150 | 2.0 | 4.0 | 9.0 | 1.0 | 7.0 | 5.0 | 3.0 | 6.0 | 10.0 | 8.0 | |
350 | 2.0 | 3.0 | 9.0 | 1.0 | 6.0 | 7.0 | 4.0 | 5.0 | 10.0 | 8.0 | |
= 2.5, | 30 | 3.0 | 2.0 | 7.0 | 1.0 | 9.0 | 4.0 | 6.0 | 10.0 | 8.0 | 5.0 |
70 | 2.0 | 5.0 | 7.0 | 1.0 | 8.0 | 3.0 | 4.0 | 10.0 | 9.0 | 6.0 | |
150 | 2.0 | 3.0 | 8.0 | 1.0 | 7.0 | 5.0 | 4.0 | 9.0 | 10.0 | 6.0 | |
350 | 2.0 | 3.0 | 8.0 | 1.0 | 6.5 | 5.0 | 4.0 | 9.0 | 10.0 | 6.5 | |
, | 30 | 3.0 | 2.0 | 8.5 | 1.0 | 6.0 | 4.0 | 5.0 | 10.0 | 8.5 | 7.0 |
70 | 2.0 | 3.0 | 7.0 | 1.0 | 8.0 | 6.0 | 4.0 | 9.0 | 10.0 | 5.0 | |
150 | 2.0 | 3.0 | 8.0 | 1.0 | 7.0 | 6.0 | 4.0 | 9.0 | 10.0 | 5.0 | |
350 | 2.0 | 3.0 | 8.0 | 1.0 | 7.0 | 6.0 | 4.0 | 9.0 | 10.0 | 5.0 | |
, | 30 | 2.0 | 3.0 | 7.5 | 1.0 | 7.5 | 6.0 | 4.0 | 9.5 | 9.5 | 5.0 |
70 | 3.0 | 2.0 | 8.0 | 1.0 | 9.0 | 5.0 | 4.0 | 7.0 | 10.0 | 6.0 | |
150 | 2.0 | 3.0 | 9.0 | 1.0 | 7.0 | 5.0 | 4.0 | 8.0 | 10.0 | 6.0 | |
350 | 2.0 | 4.0 | 7.0 | 1.0 | 8.0 | 5.0 | 3.0 | 9.0 | 10.0 | 6.0 | |
∑ Ranks | 41.0 | 61.5 | 151.5 | 24.0 | 135.5 | 118.0 | 80.5 | 160.0 | 194.0 | 134.0 | |
Overall Rank | 2 | 3 | 8 | 1 | 7 | 5 | 4 | 9 | 10 | 6 |
Model | −L | Est. Parameters (SEs) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
PHD | 58.3644 | 120.729 | 120.969 | 124.669 | 122.244 | 0.441941 | 0.0673941 | 0.119651 | 0.433879 | |
HD | 137.961 | 277.922 | 278. | 279.892 | 278.68 | 3.60152 | 0.52865 | 0.230467 | 0.00717591 | |
FD | 142.447 | 288.895 | 289.135 | 292.835 | 290.41 | 1.69303 | 0.247318 | 0.143506 | 0.225089 | |
ED | 135.988 | 273.977 | 274.055 | 275.947 | 274.734 | 2.36241 | 0.334012 | 0.211426 | 0.0175066 | |
LD | 144.572 | 291.143 | 291.222 | 293.114 | 291.901 | 6.67294 | 0.790309 | 0.280377 | 0.000481 | |
LD | 134.9 | 273.8 | 274.04 | 277.74 | 275.315 | 1.00316 | 0.154761 | 0.155981 | 0.151636 | |
MD | 244.479 | 490.958 | 491.036 | 492.928 | 491.716 | 61.0567 | 4.24272 | 0.474435 | <0.00001 | |
RD | 188.93 | 379.86 | 379.938 | 381.83 | 380.618 | 34.0881 | 3.15618 | 0.389817 | <0.00001 | |
WD | 133.395 | 270.791 | 271.031 | 274.731 | 272.306 | 0.489695 | 0.0783922 | 0.125149 | 0.377587 | |
GD | 133.439 | 270.879 | 271.119 | 274.819 | 272.394 | 0.511751 | 0.0801577 | 0.130324 | 0.328992 | |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Tashkandy, Y.; Bakr, M.E.; Gemeay, A.M.; Hussam, E.; Abd El-Raouf, M.M.; Hossain, M.M. Modeling COVID-19 Real Data Set by a New Extension of Haq Distribution. Axioms 2023, 12, 327. https://doi.org/10.3390/axioms12040327
Tashkandy Y, Bakr ME, Gemeay AM, Hussam E, Abd El-Raouf MM, Hossain MM. Modeling COVID-19 Real Data Set by a New Extension of Haq Distribution. Axioms. 2023; 12(4):327. https://doi.org/10.3390/axioms12040327
Chicago/Turabian StyleTashkandy, Yusra, Mahmoud E. Bakr, Ahmed M. Gemeay, Eslam Hussam, Mahmoud M. Abd El-Raouf, and Md Moyazzem Hossain. 2023. "Modeling COVID-19 Real Data Set by a New Extension of Haq Distribution" Axioms 12, no. 4: 327. https://doi.org/10.3390/axioms12040327