]>
2021
14
4
ISSN 2008-1898
105
Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra
Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra
en
en
Here, we investigate the existence result for a nonlinear quadratic functional integral equation of fractional order using a fixed point theorem of Dhage. The continuous dependence of solution on the delay functions will be studied. As an application, an existence theorem for the fractional hybrid differential equations is proved. Also, we study a general quadratic integral equation of fractional order.
181
195
Sh. M.
Al-Issa
Department of Mathematics, faculty of Art and Science
Department of Mathematics, faculty of Art and Science
Lebanese International University
Lebanese International University
Lebanon
Lebanon
shorouk.alissa@liu.edu.lb
N. M.
Mawed
Department of Mathematics, faculty of Art and Science
Lebanese International University
Lebanon
31430473@students.liu.edu.lb
Dhage fixed point theorem
continuous dependence of solutions
hybrid differential equations
general quadratic integral equation
Article.1.pdf
[
[1]
S. Al-Issa, A. M. A. El-Sayed, Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders, Comment. Math., 49 (2009), 171-177
##[2]
J. Banaś, J. R. Martin, K. Sadarangani, On the solution of a quadratic integral equation of Hammerstein type, Math. Comput. Model., 43 (2006), 97-104
##[3]
J. Banaś, A. Martinon, Monotonic solutions of a quadratic integral equation of Volterra type, Comput. Math. Appl., 47 (2004), 271-279
##[4]
M. A. Darwish, K. Sadarangani, Existence of solutions for hybrid fractional pantograph equations, Appl. Anal. Discrete Math., 9 (2015), 150-167
##[5]
B. C. Dhage, A fixed point theorem in Banach algebras involving three operators with applications, Kyungpook Math. J., 44 (2004), 145-155
##[6]
B. C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations, Nonlinear Funct. Anal. Appl., 9 (2004), 563-575
##[7]
B. C. Dhage, B. D. Karande, First order integro-differential equations in Banach algebras involving Caratheodory and discontinuous nonlinearities, Electron. J. Qual. Theory Differ. Equ., 2005 (2005), 1-16
##[8]
A. M. A. El-Sayed, S. M. Al-Issa, Global Integrable Solution for a Nonlinear Functional Integral Inclusion, SRX Math., 2010 (2010), 1-4
##[9]
A. M. A. El-Sayed, S. M. Al-Issa, Monotonic continuous solution for a mixed type integral inclusion of fractional order, J. Math. Appl., 33 (2010), 27-34
##[10]
A. M. A. El-Sayed, S. M. Al-Issa, Existence of continuous solutions for nonlinear functional differential and integral inclusions, Malaya J. Mat., 7 (2019), 541-544
##[11]
A. M. A. El-Sayed, S. M. Al-Issa, Monotonic integrable solution for a mixed type integral and differential inclusion of fractional orders, Int. J. Differ. Equations Appl., 18 (2019), 1-10
##[12]
A. M. A. El-Sayed, S. M. Al-Issa, Monotonic solutions for a quadratic integral equation of fractional order, AIMS Mathematics, 4 (2019), 821-830
##[13]
A. M. A. El-Sayed, S. M. Al-Issa, On a set-valued functional integral equation of Volterra-Stiltjes type, J. Math. Computer Sci., 21 (2020), 273-285
##[14]
A. El-Sayed, H. Hashem, Existence results for nonlinear quadratic integral equations of fractional order in Banach algebra, Fract. Calc. Appl. Anal., 16 (2013), 816-826
##[15]
A. El-Sayed, H. Hashem, S. Al-Issa, Existence of solutions for an ordinary second-order hybrid functional differential equation, Adv. Difference Equ., 2020 (2020), 1-10
##[16]
M. A. E. Herzallah, D. Baleanu, On Fractional Order Hybrid Differential Equations, Abstr. Appl. Anal., 2014 (2014), 1-7
##[17]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam (2006)
##[18]
M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, The American Mathematical Monthly, 75 (1964), 318-319
##[19]
W. Long, X.-J. Zhng, L. Li, Existence of periodic solutions for a class of functional integral equations, Electron. J. Qual. Theory Differ. Equ., 2012 (2012), 1-11
##[20]
S. Melliani, K. Hilal, M. Hannabou, Existence results in the theory of hybrid fractional integro-differential equations, J. Univer. Math., 1 (2018), 166-179
##[21]
M. M. A. Metwali, On a class of quadratic Urysohn-Hammerstein integral equations of mixed type and initial value problem of fractional order, Mediterr. J. Math., 13 (2016), 2691-2707
##[22]
K. S. Miller, B. Ross, An Introduction to the fractional calculus and fractional differential equations, John Wiley & Sons, New York (1993)
##[23]
I. Podlubny, Fractional Differential Equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Academic Press, San Diego (1999)
##[24]
I. Podlubny, A. M. A. EL-Sayed, On two defintions of fractional calculus, Solvak Academy Sci.-Ins. Eyperimental Phys., 1996 (1996), 3-96
##[25]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Integrals and Derivatives of Fractional Orders and Some of their Applications, Nauka i Teknika, Minsk (1987)
##[26]
Y. Zhao, S. R. Sun, Z. L. Han, Q. P. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl., 62 (2011), 1312-1324
##[27]
L. Zheng, X. Zhang, Modeling and analysis of modern fluid problems, Elsevier/Academic Press, London (2017)
]
SIQR dynamics in a random network with heterogeneous connections with infection age
SIQR dynamics in a random network with heterogeneous connections with infection age
en
en
In this paper, an SIQR-Epidemic transmission model of the non-Markovian infection process and quarantine process in a heterogeneous complex network is established, in which the infection rate and quarantine rate are related to infection age. Next, we use the method of characteristics to transform the model into an integro-differential equation and derive the epidemic threshold of the model. Finally, we focus on the impact of three different infection or quarantine time distributions on the disease transmission and show that infection or quarantine time distribution has a significant effect on the disease dynamics.
196
211
Hairong
Yan
School of Mathematical Sciences
Shanxi University
P.R. China
864415225@qq.com
Jinxian
Li
School of Mathematical Sciences
Shanxi University
P.R. China
ljxsmile1@163.com
SIQR-epidemic
complex network
infection age
non-Markovian transmission and quarantine
epidemic threshold
Article.2.pdf
[
[1]
R. M. Anderson, R. M. May, Infectious diseases of humans: dynamics and control, Oxford University Press, New York (1992)
##[2]
E. Cator, R. Van de Bovenkamp, P. Van Mieghem, Susceptible-infected-susceptible epidemics on networks with general infection and cure times, Phys. Rev. E, 87 (2013), 1-7
##[3]
S. Chen, M. Small, Y. Tao, X. Fu, Transmission Dynamics of an SIS Model with Age Structure on Heterogeneous Networks, Bull. Math. Biol., 80 (2018), 2049-2087
##[4]
S. He, Y. Peng, K. Sun, SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dyn., 101 (2020), 1667-1680
##[5]
G. Herzog, R. Redheffer, Nonautonomous SEIRS and Thron models for epidemiology and cell biology, Nonlinear Anal. Real World Appl., 5 (2004), 33-44
##[6]
W. Jing, Z. Jin, J. Zhang, An SIR pairwise epidemic model with infection age and demography, J. Biol. Dyn., 12 (2018), 486-508
##[7]
I. Z. Kiss, G. Rost, Z. Vizi, Generalization of Pairwise Models to non-Markovian Epidemics on Networks, Phys. Rev. Lett., 115 (2015), 1-5
##[8]
Q. Liu, H. Li, Global dynamics analysis of an SEIR epidemic model with discrete delay on complex network, Phys. A, 524 (2019), 289-296
##[9]
J. Liu, T. Zhang, Epidemic spreading of an SEIRS model in scale-free networks, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3375-3384
##[10]
J. Ma, Z. Ma, Epidemic threshold conditions for seasonally forced SEIR models, Math. Biosci. Eng., 3 (2006), 161-172
##[11]
M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, New York (2015)
##[12]
J. C. Miller, Epidemic size and probability in populations with heterogeneous infectivity and susceptibility, Phys. Rev. E, 76 (2007), 1-4
##[13]
J. C. Miller, A note on a paper by Erik Volz: SIR dynamics in random networks, J. Math. Biol., 62 (2011), 349-358
##[14]
N. Piovella, Analytical solution of SEIR model describing the free spread of the COVID-19 pandemic, Chaos, Solitons and Fractals, 140 (2020), 1-6
##[15]
A. Radulescu, C. Williams, K. Cavanagh, Management strategies in a seir model of COVID-19 community spread, Physics and Society, 2020 (2020), 1-21
##[16]
G. Rost, Z. Vizi, I. Z. Kiss, Pairwise approximation for SIR-type network epidemics with non-Markovian recovery, Proc. A., 474 (2018), 1-21
##[17]
N. Sherborne, J. C. Miller, K. B. Blyuss, I. Z. Kiss, Mean-field models for non-Markovian epidemics on networks, J. Math. Biol., 76 (2018), 755-778
##[18]
E. Volz, SIR dynamics in random networks with heterogeneous connectivity, J. Math. Biol., 56 (2008), 293-310
##[19]
Y. Zhang, Y. Li, Evolutionary Dynamics of Stochastic SEIR Models with Migration and Human Awareness in Complex Networks, Complexity, 2020 (2020), 1-15
##[20]
J. Zhang, D. Li, W. Jing, Z. Jin, H. Zhu, Transmission dynamics of a two-strain pairwise model with infection age, Appl. Math. Model., 71 (2019), 656-672
##[21]
J. Zhang, Z. Ma, Global dynamics of an SEIR epidemic model with saturating contact rate, Math. Biosci., 185 (2003), 15-32
##[22]
T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology, Bull. Math. Biol., 69 (2007), 2537-2559
##[23]
T. Zhou, Q. Liu, Z. Yang, J. Liao, K. Yang, W. Bai, X. Lu, W. Zhang, Preliminary prediction of the basic reproduction number of the Wuhan novel coronavirus 2019-nCoV, Evid. Based Med., 13 (2020), 3-7
##[24]
G. Zhu, X. Fu, G. Chen, Spreading dynamics and global stability of a generalized epidemic model on complex heterogeneous networks, Appl. Math. Model., 36 (2012), 5808-5817
]
\(a\)-minimal prime ideals in almost distributive lattices
\(a\)-minimal prime ideals in almost distributive lattices
en
en
The concept of \(a\)-minimal prime ideal of an ADL is introduced and its characterizations are established. The set of all \(a\)-minimal prime ideals of an ADL is topologized and resulting space is studied.
212
221
Ch. Santhi Sundar
Raj
Department of Engineering Mathematics
Andhra University
India
santhisundarraj@yahoo.com
K. Ramanuja
Rao
Deaprtment of Mathematics
Fiji National Uniersity
FIJI
ramanuja.kotti@fnu.ac.fj
S. Nageswara
Rao
Department of Engineering Mathematics
Andhra University
India
bollasubrahmanyam@gamil.com
ADL
minimal prime ideal
relative
\(a\)-annihilator
\(a\)-minimal prime ideal
\(a\)-maximal filter
\(a\)-pseudo complementation
hull-kernel topology
Article.3.pdf
[
[1]
G. Grätzer, General Lattice Theory, Academic Press, New York-London (1978)
##[2]
M. Mandelker, Relative annhilators in lattices, Duke Math. J., 37 (1970), 377-386
##[3]
G. C. Rao, S. Ravi Kumar, Minimal prime ideals in Almost Distributive Lattices, Int. J. Contemp. Math. Sci., 4 (2009), 475-484
##[4]
C. S. Sundar Raj, S. N. Rao, K. R. Rao, $\mathtt{a}$-Maximal filters in Almost Distributive Lattices, J. Int. Math. Virtual Inst., 10 (2020), 309-324
##[5]
C. S. Sundar Raj, S. N. Rao, K. R. Rao, $\mathtt{a}$-pseudo complementation on an ADL's, Asian-Eur. J. Math., 2020 (2020), -
##[6]
C. S. Sundar Raj, S. N. Rao, M. Santhi, K. R Rao, Relative pseudo-complementations on ADL'S, Int. J. Math. Soft Comput., 7 (2017), 95-108
##[7]
U. M. Swamy, G. C. Rao, Almost Distributive Lattices, J. Austral. Math. Soc. Ser A, 31 (1981), 77-91
##[8]
U. M. Swamy, G. C. Rao, G. Nanaji Rao, Pseudo-complementation on Almost Distributive Lattices, Southeast Asian Bull. Math., 24 (2000), 95-104
##[9]
J. C. Varlet, Relative annihilators in semilattices, Bull. Austral. Math. Soc., 9 (1973), 169-185
]
Generalized Kantorovich-Szász type operations involving Charlier polynomials
Generalized Kantorovich-Szász type operations involving Charlier polynomials
en
en
The purpose of this paper is to introduce a new kind of Kantorovich-Szász type operators based on Charlier polynomials and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem and an estimate of error by means of the Lipschitz type maximal function and the Peetre's K-functional. We also discuss the weighted approximation properties. Next, we construct a bivariate case of the above operators and study the degree of approximation with the aid of the complete and partial moduli of continuity. A Voronovskaja type asymptotic theorem and the order of convergence by considering the second order modulus of continuity are also proved. We define the associated Generalized Boolean Sum (GBS) operators and discuss the degree of approximation by using mixed modulus of smoothness for Bögel continuous and Bögel differentiable functions. Furthermore, by means of a numerical example it is shown that the proposed operators provide us a better approximation than the operators corresponding to the particular case \(\wp=1\). We also illustrate the convergence of the bivariate operators and the associated GBS operators to a certain function and show that the GBS operators enable us a better error estimation than the bivariate operators using Matlab algorithm.
222
249
P. N.
Agrawal
Department of Mathematics
Indian Institute of Technology Roorkee
India
pnappfma@gmail.com
Abhishek
Kumar
Department of Mathematics
Indian Institute of Technology Roorkee
India
anikk6887@gmail.com
Aditi Kar
Gangopadhyay
Department of Mathematics
Indian Institute of Technology Roorkee
India
aditifma@iitr.ac.in
Tarul
Garg
Department of Applied Science
The NorthCap University
India
tarulgarg@ncuindia.edu
Voronovskaya theorem
moduli of continuity
Peetre's K-functional
Bögel continuous function
Bögel differentiable function
Article.4.pdf
[
[1]
P. N. Agrawal, N. Ispir, Degree of approximation for bivariate Chlodowsky-Szasz-Charlier type operators, Results. Math., 69 (2016), 369-385
##[2]
C. Badea, K-Functionals and moduli of smoothness of functions defined on compact metric spaces, Comput. Math. Appl., 30 (1995), 23-31
##[3]
C. Badea, I. Badea, H. Gonska, Notes on the degree of approximation of B-continuous and B-differentiable functions, J. Approx. Theory Appl., 4 (1988), 95-108
##[4]
C. Badea, C. Cottin, Korovkin-type theorems for generalised Boolean sum operators, Approx. Theory (Kecskemat, Hungary), Colloq. Math. Soc. Janos Bolyai, 58 (1990), 51-67
##[5]
D. Barbosu, C. V. Muraru, Approximating B-continuous functions using GBS operators of Bernstein-Schurer-Stancu type based on q-integers, Appl. Math. Comput., 259 (2015), 80-87
##[6]
K. Bogel, Mehrdimensionale Differentiation von Funktionen mehrerer reeller Veränderlichen, J. Reine Angew. Math., 170 (1934), 197-217
##[7]
K. Bogel, Über mehrdimensionale Differentiation, Integration und beschränkte Variation, J. Reine Angew. Math., 173 (1935), 5-30
##[8]
K. Bogel, Über die mehrdimensionale differentiation, Jber. Deutsch. Math.-Verein., 65 (1962), 45-71
##[9]
P. L. Butzer, H. Berens, Semi-groups of Operators and Approximation, Springer-Verlag, New York (1967)
##[10]
R. A. Devore, G. G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin (1993)
##[11]
Z. Ditzian, V. Totik, Moduli of Smoothness, Springer-Verlag, New York (1987)
##[12]
E. Dobrescu, I. Matei, The approximation by Bernstein type polynomials of bidimensionally continuous functions, An. Univ. Timis¸oara Ser. S¸ ti. Mat.-Fiz., 4 (1996), 85-90
##[13]
A. D. Gadzhiev, Theorems of Korovkin type, Math. Notes, 20 (1976), 995-998
##[14]
V. Gupta, T. M. Rassias, P. N. Agrawal, A. M. Acu, Recent Advances in Constructive Approximation Theory, Springer, Cham (2018)
##[15]
E. Ibikli, E. A. Gadjiev, The order of approximation of some unbounded functions by the sequences of positive linear operators, Turkish J. Math., 19 (1995), 331-337
##[16]
B. Lenze, On Lipschitz-type maximal functions and their smoothness spaces, Indag. Math., 53--63 (1988), -
##[17]
M. A. Ozarslan, H. Aktuglu, Local approximation properties for certain King type operators, Filomat, 27 (2013), 173-181
##[18]
M. A. Ozarslan, O. Duman, Smoothness properties of modified Bernstein-Kantorovich operators, Numer. Funct. Anal. Optim., 37 (2016), 92-105
##[19]
J. Peetre, Theory of Interpolation of Normal Spaces, Lecture Notes, Brasilia (1963)
##[20]
O. Szasz, Generalization of S. Bernstein’s polynomials to be infinite interval, J. Res. Natl. Bur. Stand., 45 (1952), 239-245
##[21]
B. S. Theodore, H. Hsu, A Non-linear Transformation for Sequences and Integrals, Thesis Master Sci., Graduate Faculty of Texas Thechnological College (1968)
##[22]
S. Varma, F. Taşdelen, Szász type operators involving Charlier polynomials, Math. Comput. Model, 56 (2012), 118-122
]
The Marshall-Olkin-Gompertz-G family of distributions: properties and applications
The Marshall-Olkin-Gompertz-G family of distributions: properties and applications
en
en
We develop a new generalized family of the Gompertz-G distribution, namely, the Marshall-Olkin-Gompertz-G distribution. Statistical properties of the new proposed model are presented. Some special cases of the new family of distributions are presented. Maximum likelihood estimates of the model parameters are also determined. A simulation study was conducted to assess the performance of the maximum likelihood estimates. Applications to demonstrate the usefulness of the Marshall-Olkin-Gompertz-Weibull distribution to real data examples are provided.
250
267
Fastel
Chipepa
Department of Mathematical Statistics
Department of Applied Mathematics and Statistics
Botswana International University of Science and Technology
Midlands State University
Botswana
Zimbabwe
chipepaf@staff.msu.ac.zw
Broderick
Oluyede
Department of Mathematical Statistics
Botswana International University of Science and Technology
Botswana
oluyedeo@biust.ac.bw
Gompertz-G distribution
Marshall-Olkin-G distribution
maximum likelihood estimation
Article.5.pdf
[
[1]
M. Alizadeh, L. Benkhelifa, M. Rasekhi, B. Hosseini, The odd log-logistic generalized Gompertz distribution: Properties, applications and different methods of estimation, Commun. Math. Stat., 8 (2020), 295-317
##[2]
M. Alizadeh, G. M. Cordeiro, L. G. Bastos Pinho, I. Ghosh, The Gompertz-G family of distributions, J. Stat. Theory Pract., 11 (2017), 179-207
##[3]
M. Alizadeh, S. Tahmasebi, M. R. Kazemi, H. S. A. Nejad, G. H. G. Hamedani, The odd log-logistic Gompertz lifetime distribution: Properties and applications, Studia Sci. Math. Hungar., 56 (2019), 55-80
##[4]
W. Barreto-Souza, H. S. Bakouch, A New Lifetime Model with Decreasing Failure Rate, Statistics, 47 (2013), 465-476
##[5]
W. Barreto-Souza, A. J. Lemonte, G. M. Cordeiro, General results for the Marshall and Olkin’s family of distributions, An. Acad. Brasil. Cienc., 85 (2013), 3-21
##[6]
M. Bourguignon, R. B. Silva, G. M. Cordeiro, The Weibull-G family of probability distributions, J. Data Sci., 12 (2014), 53-68
##[7]
J. M. Chambers, W. S. Cleveland, B. Kleiner, P. A. Tukey, Graphical Methods of Data Analysis, Inter. Bio. Soc., 40 (1984), 567-568
##[8]
F. Chipepa, B. Oluyede, B. Makubate, The Odd Generalized Half-Logistic Weibull-G Family of Distributions: Properties and Applications, Journal of Statistical Modelling: Theory and Applications, 2020 (2020), 1-25
##[9]
F. Chipepa, B. Oluyede, B. Makubate, A. Fagbamigbe, The Beta Odd Lindley-G Family of Distributions with Applications, J. Probab. Stat. Sci., 17 (2019), 51-83
##[10]
F. Chipepa, B. Oluyede, B. Makubate, A New Generalized Family of Odd Lindley-G Distribution with application, Int. J. Stat. Probab., 8 (2019), 1-23
##[11]
F. Chipepa, B. Oluyede, D. Wanduku, The Exponentiated Half Logistic Odd Weibull-Topp-Leone-G Family of Distributions: Model, Properties and Applications, Journal of Statistical Modelling: Theory and Applications, 2020 (2020), -
##[12]
G. M. Cordeiro, M. Alizadeh, P. R. D. Marinho, The type I half-logistic family of distributions, J. Stat. Comput. Simul., 86 (2016), 707-728
##[13]
G. M. Cordeiro, M. Alizadeh, A. D. C. Nascimento, M. Rasekhi, The Exponentiated Gompertz Generated Family of Distributions: Properties and Applications, Chil. J. Stat., 7 (2016), 29-50
##[14]
G. M. Cordeiro, M. de Castro, A New Family of Generalized Distributions, J. Stat. Comput. Simul., 81 (2011), 883-898
##[15]
G. M. Cordeiro, E. M. M. Ortega, S. Nadarajaah, The Kumaraswamy Weibull Distribution with Application to Failure Data, J. Franklin Inst., 347 (2010), 1399-1429
##[16]
A. El-Gohary, A. Alshamrani, A. N. Al-Otaibi, The Generalized Gompertz Distribution, Appl. Math. Model., 37 (2013), 13-24
##[17]
N. Eugene, C. Lee, F. Famoye, Beta-Normal Distribution and Its Applications, Comm. Statist. Theory Methods, 31 (2002), 497-512
##[18]
J. U. Gleaton, J. D. Lynch, Properties of Generalized Log-Logistic Families of Lifetime Distributions, JPSS J. Probab. Stat. Sci., 4 (2006), 51-64
##[19]
B. Gompertz, On the Nature of the Function Expressive of the Law of Human Mortality and on the New Mode of Determining the Value of Life Contingencies, Philos. Trans. Roy. Stat. Soc., 115 (1825), 413-580
##[20]
W. Gui, Marshall-Olkin Extended Log-logistic Distribution and Its Application in Minification Processes, Appl. Math. Sci., 7 (2013), 3947-3961
##[21]
R. D. Gupta, D. Kundu, Generalized Exponential Distributions, Aust. N. Z. J. Stat., 41 (1999), 173-188
##[22]
M. R. Gurvich, A. T. DiBenedetto, S. V. Ranade, A New Statistical Distribution for Characterizing the Random Strength of Brittle Materials, J. Mater. Sci., 32 (1997), 2559-2564
##[23]
A. A. Jafari, S. Tahmasebi, M. Alizadeh, The beta-Gompertz distribution, Rev. Colombiana Estadıst., 37 (2014), 141-158
##[24]
H. Karamikabir, M. Afshari, M. Alizadeh, G. G. Hamedani, A new extended generalized Gompertz distribution with statistical properties and simulations, Comm. Statist. Theory Methods, 2019 (2019), 1-29
##[25]
M. C. Korkmaz, H. M. Yousof, G. G. Hamedani, The Exponential Lindley Odd Log-Logistic-G family: Properties, Characterizations and Applications, J. Stat. Theory Appl., 17 (2018), 554-571
##[26]
A. W. Marshall, I. Olkin, A New Method for Adding a Parameter to a Family of Distributions with Applications to the Exponential and Weibull Families, Biometrika, 84 (1997), 641-652
##[27]
R. M. Pakungwati, Y. Widyaningsih, D. Lestari, Marshall-Olkin Extended Inverse Weibull Distribution and Its Application, J. Phys.: Conf. Ser., 1108 (2018), 1-7
##[28]
R. C. Team, R: a Language and Environment for Statistical Computing, , (2013)
##[29]
A. Renyi, On Measures of Entropy and Information, Univ. California Press, Berkeley, Calif., 1960 (1960), 547-561
##[30]
M. M. Ristic, N. Balakrishnan, The Gamma Exponentiated Exponential Distribution, J. Stat. Comput. Simul., 82 (2012), 1191-1206
##[31]
M. Shaked, J. G. Shanthikumar, Stochastic Orders, Springer, New York (2007)
##[32]
C. E. Shannon, Prediction and Entropy of Printed English, Bell Syst. Tech. J., 30 (1951), 50-64
##[33]
R. L. Smith, J. C. Naylor, A Comparison of Maximum Likelihood and Bayesian Estimators for the Three-Parameter Weibull Distribution, Appl. Statist., 36 (1967), 358-369
##[34]
H. Torabi, N. M. Hedesh, The Gamma-Uniform Distribution and Its Applications, Kybernetika, 48 (2012), 16-30
##[35]
K. Xu, M. Xie, L. C. Tang, S. L. Ho, Application of Neural Networks in Forecasting Engine Systems reliability, Appl. Soft. Comput., 2 (2003), 255-268
##[36]
K. Zografos, N. Balakrishnan, On Families of Beta- and Generalized Gamma-Generated Distributions and Associated Inference, Stat. Methodol., 6 (2009), 344-362
]
The odd Weibull-Topp-Leone-G power series family of distributions: model, properties, and applications
The odd Weibull-Topp-Leone-G power series family of distributions: model, properties, and applications
en
en
A new generalization of the odd Weibull-Topp-Leone-G family of distributions called the odd Weibull-Topp-Leone-G power series family of distributions is developed. Statistical properties of the new distribution were derived. We also derive the maximum likelihood estimates of the proposed model. Some special cases for the new family of distributions were also considered. We conducted a simulation study to evaluate the consistency of the maximum likelihood estimates. Two real data examples were also considered to demonstrate the usefulness of the newly proposed family of distributions.
268
286
Broderick Oluyede
Department of Mathematical Statistics
Botswana International University of Science and Technology
Botswana
oluyedeo@biust.ac.bw
Fastel
Chipepa
Department of Mathematical Statistics
Department of Applied Mathematics and Statistics
Botswana International University of Science and Technology
Midlands State University
Botswana
Zimbabwe
chipepaf@staff.msu.ac.zw
Divine
Wanduku
Department of Mathematical Sciences
Georgia Southern University
USA
dwanduku@georgiasouthern.edu
Odd Weibull-Topp-Leone-G
odd Weibull-G
Topp-Leone-G distribution
power series distribution
Article.6.pdf
[
[1]
O. O. Aalen, Heterogeneity in Survival Analysis, Statistics in Medicine, 7 (1988), 1121-1137
##[2]
M. A. D. Aldahlan, A. Z. Afify, The odd exponentiated half-logistic Burr XII distribution, Pak. J. Stat. Oper. Res., 14 (2018), 305-317
##[3]
M. Alizadeh, A. Z. Afify, M. S. Eliwa, S. Ali, The Odd Log-Logistic Lindley-G Family of Distributions: Properties, Bayesian and Non-Bayesian Estimation with Applications, Comput. Stat., 35 (2020), 281-308
##[4]
Z. A. Al-Saiary, R. A. Bakoban, The Topp-Leone Generalized Inverted Exponential Distribution with Real Data Applications, Entropy, 22 (2020), 1-15
##[5]
A. Al-Shomrani, O. Arif, A. Shawky, S. Hanif, M. Q. Shahbaz, Topp-Leone family of distributions: Some properties and application, Pak. J. Stat. Oper. Res., 12 (2016), 443-451
##[6]
R. G. Aryal1, E. M. Ortega, G. G. Hamedani, H. M. Yousof, The Topp-Leone Generated Weibull Distribution: Regression Model, Characterizations and Applications, Int. J. Stat. Prob., 6 (2017), 126-141
##[7]
H. Bidram, V. Nekoukhou, Double Bounded Kumaraswamy-Power Series Class of Distributions, SORT, 37 (2013), 211-230
##[8]
F. Chipepa, B. Oluyede, S. Chamunorwa, The odd Weibull-Topp-Leone-G Family of Distributions: Model, Properties and Applications, To Appear, (2020)
##[9]
F. Chipepa, B. O. Oluyede, B. Makubate, A New Generalized Family of Odd Lindley-G Distributions with Application, Int. J. Stat. Prob., 8 (2019), 1-23
##[10]
F. Chipepa, B. Oluyede, B. Makubate, The Odd Generalized Half-Logistic Weibull-G Family of Distributions: Properties and Applications, J. Stat. Model. Theor. Appl., 2020 (2020), 1-25
##[11]
F. Chipepa, B.Oluyede, B. Makubate, The Topp-Leone-Marshall-Olkin-G Family of Distributions with Applications, Int. J. Stat. Prob., 9 (2020), 15-32
##[12]
F. Chipepa, B. Oluyede, B. Makubate, A. Fagbamigbe, The Beta Odd Lindley-G Family of Distributions with Applications, J. Prob. Stat. Sci., 17 (2019), 51-84
##[13]
G. M. Cordeiro, A. E. Gomes, C. Q. da-Silva, E. M. M. Ortega, The Beta Exponentiated Weibull Distribution, J. Stat. Comput. Simul., 83 (2013), 114-138
##[14]
G. M. Cordeiro, E. M. M. Ortega, S. Nadarajaah, The Kumaraswamy Weibull Distribution with Application to Failure Data, J. Franklin Inst., 347 (2010), 1399-1429
##[15]
G. M. Cordeiro, R. B. Silva, The Complementary Extended Weibull Power Series Class of Distributions, Ciência e Natura, 36 (2014), 1-13
##[16]
F. Gomes-Silva, A. Percontini, E. de Brito, M. W. Ramos, R Venancio, G. M. Cordeiro, The odd Lindley-G family of distributions, Aust. J. Stat., 46 (2017), 65-87
##[17]
I. S. Gradshetyn, I. M. Ryzhik, Tables of Integrals, Series and Products, Sixth edition, Academic Press, San Diego (2000)
##[18]
M. R. Gurvich, A. T. DiBenedetto, S. V. Ranade, A New Statistical Distribution for Characterizing the Random Strength of Brittle Materials, J. Mat. Sci., 32 (1997), 2559-2564
##[19]
S. S. Harandi, M. H. Alamatsaz, Generalized Linear Failure Rate Power Series Distribution, Comm. Statist. Theory Methods, 45 (2016), 2204-2227
##[20]
M. Ibrahim, H. Yousof, Transmuted Topp-Leone Weibull Lifetime Distribution: Statistical Properties and Different Method of Estimation, Pak. J. Stat. Oper. Res., 16 (2020), 501-515
##[21]
N. L. Johnson, S. Kotz, N. Balakrishnan, Continuous univariate distributions, John Wiley & Sons, New York (1994)
##[22]
B. Jorgensen, Statistical Properties of the Generalized Inverse Gaussian Distribution, Springer-Verlag, New York (1982)
##[23]
M. C. Korkmaz, H. M. Yousof, G. G. Hamedani, The Exponential Lindley Odd Log-Logistic-G Family: Properties, Characterizations and Applications, J. Stat. Theory Appl., 17 (2018), 554-571
##[24]
E. Mahmoudi, A. A. Jafari, Generalized Exponential-Power Series Distributions, Comput. Statist. Data Anal., 56 (2012), 4047-4066
##[25]
E. Mahmoudi, A. A. Jafari, The Compound Class of Linear Failure Rate-Power Series Distributions: Model, Properties, and Applications, Comm. Statist. Simulation Comput., 46 (2017), 1414-1440
##[26]
A. L. Morais, W. Barreto-Souza, A Compound Class of Weibull and Power Series Distributions, Comput. Statist. Data Anal., 55 (2011), 1410-1425
##[27]
F. A. Pena-Ramirez, R. R. Guerra, G. M. Cordeiro, P. R. D. Marinho, The Exponentiated Power Generalized Weibull: Properties and Applications, An. Acad. Brasil. Ciênc., 90 (2018), 2553-2577
##[28]
A. Rényi, On Measures of Entropy and Information, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Univ. California Press, Berkeley, 1961 (1961), 547-561
##[29]
C. E. Shannon, Prediction and Entropy of Printed English, The Bell System Technical J., 30 (1951), 50-64
##[30]
R. B. Silva, M. Bourguignon, C. R. B. Dias, G. M. Cordeiro, The Compound Class of Extended Weibull Power Series Distributions, Comput. Statist. Data Anal., 58 (2013), 352-367
##[31]
R. B. Silva, G. M. Cordeiro, The Burr XII Power Series Distributions: A New Compounding Family, Braz. J. Probab. Stat., 29 (2015), 565-589
]