Dr. EHIWARIO JACOB CHINEDUM
Publication Title A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications
Publication Type journal
Publisher Wiley International Journal of Mathematics and Mathematical Sciences Volume 2024, Article ID 5583105, 23 pages https://doi.org/10.1155/2024/5583105
Paper Link https://doi.org/10.1155/2024/5583105
Publication Authors Simon A. Ogumeyo , 1 Festus C. Opone , 2 Abdul Ghaniyyu Abubakari , 3 and Jacob C. Ehiwario4
Year Published 2024-07-17
Abstract Trigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. Tis is due
to their parsimonious framework, mathematical tractability, and fexibility of the newly developed distributions. In this paper, the
Sine-generated family is used to create a new bounded lifetime distribution, known as Sine-Marshall–Olkin Topp–Leone
distribution, for modeling data defned on the unit interval. Some statistical properties of the new bounded distribution, including
quantile function, ordinary moments, incomplete moments, moment-generating functions, inequality measures, Renyi entropy, ´
and probability weighted moments are derived. Seven methods of parameter estimation, including maximum likelihood, ordinary
least squares, weighted least squares, moment product spacing, Anderson–Darling, and Cramer–von Mises estimators are used to ´
estimate the parameters of the new distribution. Te behavior of the estimators obtained from the estimation methods are
investigated using Monte Carlo simulation studies. Te results show that the estimation methods are asymptotically efcient and
consistent. Te fexibility of the new bounded distribution is examined via data ftting using two proportional datasets. Te results
of the fttings show that the new bounded distribution performs signifcantly better than the competing bounded lifetime
distributions. Finally, Sine-Marshall–Olkin Topp–Leone regression model is presented as an alternative to the beta and
Kumaraswamy regression models.
Publication Title Mathematically Modeling the Telephone and Telegraph Equations in a Long Cable or Transmission Line
Publication Type journal
Publisher International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume V, Issue VIII, August 2020|ISSN 2454-6194
Paper Link http://www.rsisinternational.org/
Publication Authors S.I Nwakaego*, J.C Ehiwario, Dr C.E. Emenonye
Year Published 2020-08-08
Abstract This paper presents a mathematical model of the
telephone and telegraph equations in a transmission line. The
flow of electricity in a transmission line was considered. It was
observed that waves and wave propagation are ubiquitous in
nature and lead to many puzzling questions. For example, why is
it that a storm over the ocean sets off a steady swell of smallamplitude waves, but an earthquake at the sea floor can release
an enormous flood wave? What produces mirages in the desert?
In response to these questions, a great deal of mathematics has
been developed to understand and predict the dynamics of light
or sound waves the propagation of matter waves, the vibration
patterns of elastic bodies, or the peculiar nature of water waves.
This paper will provide a guided tour of mathematical wave
theory together with physical applications, including the linear
wave equation, dispersion and nonlinear waves and solitons.
Mathematically one – dimensional heat equations for the flow
were derived.
Publication Title THEORY AND APPLICATIONS OF THE ALPHA POWER TYPE II TOPP-LEONE- GENERATED FAMILY OF DISTRIBUTIONS
Publication Type journal
Publisher THE APTIITL-G FAMILY OF DISTRIBUTIONS RT&A, No.3 (74) Volume 18, September 2023
Publication Authors Jacob C. Ehiwario1 John N. Igabari2 Peter E. Ezimadu3
Year Published 2023-09-09
Abstract This paper introduces a composition of two single parameter generalized family of
distributions: the alpha power transform and type II Topp-Leone-G families of
distributions. Some basic mathematical treatments of the family of distributions are
studied. The parameter estimates of the proposed family of distributions are derived via
maximum likelihood estimation method and a Monte Carlo simulation study was
conducted to examine the asymptotic behaviour of the parameter estimates of sub-model
belonging to the proposed family of distributions. To illustrate the applicability of the
proposed family of distributions in real world data fittings, two data sets consisting of the
daily recovery and mortality rates of Covid-19 patients in Nigeria, from May 1 to June 30,
2020, was employed. The APTIITLK distribution arising from the proposed family of
distributions, alongside with some bounded non-nested distributions was used to fit the
two data sets and results obtained from the analysis clearly revealed that the APTIITLK
distribution outperformed all the non-nested distributions used in fitting the two data sets.
Some informative graphical plots for goodness of fit test were investigated to further
validate the flexibility of the APTIITLK distribution over the competing distributions.
Publication Title The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications
Publication Type journal
Publisher Journal of Applied Mathematics and Physics, 2023, 11, 316-331 https://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352
Paper Link https://doi.org/10.4236/jamp.2023.111018
Publication Authors Jacob C. Ehiwario1*, John N. Igabari2, Peter E. Ezimadu2
Year Published 2023-11-11
Abstract This paper presents an extended lifetime probability distribution based on the
alpha power transformation. We refer to the proposed distribution as “the
Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of
the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments
and its relative measures, probability weighted moment, moment generating
function, Renyi entropy, and the distribution of order statistics were derived.
The method of maximum likelihood estimation was employed to estimate the
unknown parameters of the APTL distribution. Finally, we used two real data
sets obtained from the literature to illustrate the applicability of the APTL
distribution in real-life data fitting
Publication Title Exploring a New Lifetime Distribution for Modelling the Waiting Time of Bank Customers
Publication Type journal
Publisher Journal of Applied Mathematics and Physics, 2024, 12, 194-209 https://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352
Paper Link https://doi.org/10.4236/jamp.2024.121015
Publication Authors Simon A. Ogumeyo1, Jacob C. Ehiwario2, Festus C. Opone3*
Year Published 2024-01-30
Abstract The fitting of lifetime distribution in real-life data has been studied in various
fields of research. With the theory of evolution still applicable, more complex
data from real-world scenarios will continue to emerge. Despite this, many researchers have made commendable efforts to develop new lifetime distributions
that can fit this complex data. In this paper, we utilized the KM-transformation
technique to increase the flexibility of the power Lindley distribution, resulting in the Kavya-Manoharan Power Lindley (KMPL) distribution. We study
the mathematical treatments of the KMPL distribution in detail and adapt the
widely used method of maximum likelihood to estimate the unknown parameters of the KMPL distribution. We carry out a Monte Carlo simulation
study to investigate the performance of the Maximum Likelihood Estimates
(MLEs) of the parameters of the KMPL distribution. To demonstrate the effectiveness of the KMPL distribution for data fitting, we use a real dataset
comprising the waiting time of 100 bank customers. We compare the KMPL
distribution with other models that are extensions of the power Lindley distribution. Based on some statistical model selection criteria, the summary results of the analysis were in favor of the KMPL distribution. We further investigate the density fit and probability-probability (p-p) plots to validate the superiority of the KMPL distribution over the competing distributions for fitting the waiting time dataset.
Publication Title The Impact of the Lockdown Measure on the Confirmed Cases of the Novel Coronavirus (COVID-19) in Nigeria
Publication Type journal
Publisher Journal of Scientific Research & Reports 26(6): 110-119, 2020; Article no.JSRR.59393 ISSN: 2320-0227
Paper Link DOI: 10.9734/JSRR/2020/v26i630276
Publication Authors Charles Okechukwu Aronu1*, Nkechi Udochukwu Otty2 , Jacob Chinedum Ehiwario3 and Patrick Nnaemeka Okafor4
Year Published 2020-08-05
Abstract Aims: This study examined the impact of the lockdown measure on the confirmed cases of the
Novel Coronavirus (COVID-19) in Nigeria. The objectives of the study include to identifying an
appropriate autoregressive integrated moving average (ARIMA) model that is adequate for
estimating the reported cases of COVID-19 in Nigeria and to ascertain whether the ease of
lockdown has a significant impact on the reported cases of COVID-19 in Nigeria.
Place and Duration of Study: The source of the data used for this study was the secondary data
obtained from the daily report of the United Nations Office for the Coordination of Humanitarian
Affairs (OCHA) from 1st February 2020 to 30th June 2020.
Methodology: The statistical tools used for data analysis are the ARIMA time series model and the
Chow test analysis.
Results: Nigeria ranked 1st in West Africa sub-region with a total of 25, 133 confirmed COVID-19
cases, followed by Ghana with 17, 351 confirmed cases while Gambia recorded the least number
of confirmed cases with 47 cases of COVID19. The ARIMA (0, 1, 1) was identified as the best
model for forecasting the confirmed COVID-19 cases in Nigeria within the observed period. It was
found that there exists a significant difference in the number of confirmed cases of COVID-19
during the lockdown period and the post lockdown period.
Conclusion: The study revealed that Nigeria has the most confirmed cases of COVID-19 in West
Africa region. Also, the ease of the lockdown was found to increase the number of confirmed virus
cases in Nigeria.
Publication Title The robustness of F-test in two-way interactive balanced design
Publication Type journal
Publisher Discrete Mathematics Elixir Dis. Math. 92 (2016) 39301-39304
Paper Link http://www.elixirpublishers.com/
Publication Authors Ehiwario, J.C1 , Osemeke, R.F1 and Okafor Nnaemeka P2
Year Published 2016-03-29
Abstract The extent of departure of a set of data from the fundamental assumptions required by a test
is often very important in the determination of the appropriate statistical test to be applied.
Some test statistics are more robust to the departure from certain underlying assumptions
than others. Hence, the study was aimed at examining the robustness or non-robustness of
the F-test statistic in the two-way Interactive Balanced Design. The data used for the study
were tested against the three basic assumptions of analysis of variance which include
normality, independence and homogeneity of variance assumptions. The results show that
even when the normality and homogeneity of variance assumptions were violated, the F-test
still yields good results. Hence, it was concluded that the F-test is robust to the normality
and homogeneity of variance assumptions. Based on the results of the study, it was
recommended that large sample size should always be used in carrying out any experiment
involving the applications of analysis of variance. It was also recommended that the rank
transformation is a step in the right direction whenever our data fail to conform with the
assumptions of ANOVA prior to the conventional ANOVA test since it yields result in test
which are more robust to the non-normal and resistance to outliers and non-homogeneity of
variance.
Publication Title Hirerachical Decision Making Under Uncertainty In Relation To Telecommunication Industries
Publication Type journal
Publisher INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 9, SEPTEMBER 2014 ISSN 2277-8616
Paper Link http://www.ijstr.org/
Publication Authors Azagbaekwue, A , Ehiwario, J.C, Emenoye, C.E
Year Published 2014-09-09
Abstract : In this study, our interest was on the effect of decisions resulting from different decision makers who are independent actors and their major
aim is to maximize profit in an uncertain market environment. Every firm set its decisions in the future period as a response to its competitor’s policy. We
employ stochastic programming and operators’ model in modeling the situation. A structured model in a telecommunication environment for virtual
network operators (VNO) was used without their own network facilities.
Publication Title A REVIEW ON THE LINDLEY FAMILY OF DISTRIBUTIONS
Publication Type journal
Publisher Nigerian Journal of Science and Environment 2022 Vol 20 (2) 68 - 80
Publication Authors Opone C. Festus1 , *Meninwa A. Collins2 , Ehiwario C. Jacob3
Year Published 2022-02-02
Abstract The Lindley distribution is one of the statistical distributions widely used in
modeling real lifetime data, but notably due to the monotonic property of the
hazard rate function, the distribution fails to provide good fit for certain data set
of interest. In order to address this situation, researchers have keenly been
attracted to the act of developing generalized distributions with the aim of
increasing the flexibility of the classical Lindley distribution. This paper presents
a review on some methods of developing new generalization of lifetime
distributions, in particular, the Lindley family of distributions. The applicability
of some well-known generalized Lindley distributions is illustrated using a real
data set, and the Maximized log-likelihood (Log-Lik), Akaike information
criterion (AIC), Kolmogorov-Smirnov (K-S) test Statistic, Anderson Darling (A*
)
test Statistic, Crammer von mises (W*
) test Statistic and Probability-Probability
(P-P) plots were used as criteria for comparison.
Publication Title A COMPARATIVE STUDY ON THE ALPHA POWER TRANSFORMED FAMILY OF DISTRIBUTIONS
Publication Type journal
Publisher Abacus (Mathematics Science Series) Vol. 49, No 3, September. 2022
Publication Authors Jacob C. Ehiwario1 , John N. Igabari2 and Jophet E. Okoh3
Year Published 2022-09-03
Abstract In the theory of statistical analysis, it is indisputable to state that the flexibility of statistical
distributions are enhanced through the addition of extra parameter(s). Several methods have been
introduced in literature. Nevertheless, not all methods are suitable to enhance the flexibility of existing
models.In this paper, we present a comparative study on the alpha power family of distributions. More
specifically, the Weibull, log-logistic, Bur II, power4Lindley, Gompertz distributions, and their
corresponding alpha power transformed versions are studied. Some of the mathematical properties
of the distributions are discussed and three real data sets were used to examine the effect of the extra
parameter in the alpha power transformed method on the baseline distributions.
Publication Title Comparative Study of Bisection, Newton-Raphson and Secant Methods of Root- Finding Problems
Publication Type journal
Publisher IOSR Journal of Engineering (IOSRJEN) www.iosrjen.org ISSN (e): 2250-3021, ISSN (p): 2278-8719 Vol. 04, Issue 04 (April. 2014), ||V1|| PP 01-07
Paper Link http://www.iosrjen.org/
Publication Authors Ehiwario, J.C., Aghamie, S.O.
Year Published 2014-04-04
Abstract The study is aimed at comparing the rate of performance, viz-aviz, the rate of convergence of
Bisection method, Newton-Raphson method and the Secant method of root-finding. The software, mathematica
9.0 was used to find the root of the function, f(x)=x-cosx on a close interval [0,1] using the Bisection method,
the Newton’s method and the Secant method and the result compared. It was observed that the Bisection method
converges at the 52 second iteration while Newton and Secant methods converge to the exact root of 0.739085
with error 0.000000 at the 8th and 6th iteration respectively. It was then concluded that of the three methods
considered, Secant method is the most effective scheme. This is in line with the result in our Ref.[4].
Publication Title QUEUEING THEORY IN SOLVING TELE-TRAFFIC PROBLEM
Publication Type journal
Publisher FUDMA Journal of Sciences (FJS) ISSN online: 2616-1370 ISSN print: 2645 - 2944 Vol. 6 No. 4, August, 2022, pp 191 - 194
Paper Link https://doi.org/10.33003/fjs-2022-0601-xxx
Publication Authors *Emenonye, E. C., Nwakego, S. O. and Ehiwario, J. C.
Year Published 2022-08-08
Abstract Information technology has made the world a global village and tele communication plays an indispensible
role in this. Queues are predominant features in information processing and transfer. This work examines queue
model in relation to telecommunication transfer/ processing problems. Some of the prevalent questions in teletraffic are “how do we minimize time wastage (how long do I wait?) in the system and what will be the effect
on waiting time if the number of operations are altered. In this work, tele-traffic problem was formulated and
solution established through a model. Focasting ideas were also suggested. The queue theory has been applied
to answer the above questions. The model has shown increased service satisfaction and in turn minimizes cost.
Publication Title COMMON F-TEST DENOMINATOR FOR TWO-WAY INTERACTIVE BALANCED DESIGN
Publication Type journal
Publisher Natural and Applied Sciences Journal, Vol. 10 No. 2 2009 Available online at www.naasjournal-ng.org.
Paper Link http://www.naasjournal-ng.org/
Publication Authors Eze F. C. Ehiwario J.C. and Ogum G.E.O
Year Published 2009-02-02
Abstract The presence of interaction in a set of data/model gives rise to the problem of
difference in F-test denominator for two-way interactive balanced design. This
forms the core focus of this paper. The least square estimate of the parameter
and the expected mean squares for the full and reduced models were derived.
When the interaction effects were removed from the full model, we obtained
the reduced model and consequently introduced heterogeneity of Variance,
which is a complete violation of the ANOVA assumption. An error Variance
was then derived and used to normalize the effects of the distorted
assumption. This was done by dividing the sum of squares of the main effects
and the error of the full model by the square root of the error Variance before
carrying out the test for significance on the main effects. The result shows that
the reduced model yielded the same result with full model. It was
recommended that the reduced model should be used whenever there is
interaction in our data/model. This is true for two main reasons: - (i) It is more
efficient relative to the full model. (ii) The reduced model helps to solve the
problem of differences in F-test denominator.
Publication Title ASCERTAINING PERFORMING AND NON-PERFORMING LOAN POTENTIALS IN COOPERATIVE SOCIETIES USING DESCRIPTIVE DISCRIMINANT ANALYSIS.
Publication Type journal
Publisher COOU Journal of Physical Sciences 7 (1), 2024
Paper Link http://www.cjps.coou.edu.ng/
Publication Authors 1Fortune MEKA, 1Jacob Chiedum Ehiwario, 2John N. Igabari
Year Published 2024-07-07
Abstract The issue of non-performance of loans (a situation by which a borrower fails to repay
his collected loan) has become a concern to cooperative societies. In this study,
methods and results of analyzing loan performance by borrowers was emphasized.
Descriptive Discriminant Analysis was used to reveal variables that separate loan
applicants who can pay back and those who may find it difficult to pay back. The
data for this study was collected from cooperative societies of selected tertiary
institutions for a period of 5 years, 2018 to 2022. 7 variables generated from
information on the loan forms were used from a sample of 30 past applicants who
paid well (performing loan) and 30 who did not pay well (non- performing loan).
The 30 by 7 matrices for the two groups were analyzed using SPSS. The result shows
that the variables with the highest discriminating powers were net salary,
department of guarantor and accumulated fund of applicant.