The Marshall-olkin Inverse Lomax Distribution (MO-ILD) with Application on Cancer Stem Cell

2019 ◽  
pp. 1-12 ◽  
Author(s):  
Obubu Maxwell ◽  
Angela Unna Chukwu ◽  
Oluwafemi Samuel Oyamakin ◽  
Mundher A. Khaleel
Keyword(s):  
Stem Cell ◽  
Cancer Stem Cell ◽  
Weibull Distribution ◽  
Model Parameters ◽  
Data Types ◽  
Lomax Distribution ◽  
Method Of Maximum Likelihood ◽  
Compound Distribution ◽  
Inverse Lomax Distribution ◽  
Cell Data

A new compound distribution called the Marshall-Olkin Inverse Lomax distribution (MO-ILD) was proposed, extending the inverse Lomax distribution by adding a new parameter to the existing distribution, leading to greater flexibility in modeling various data types. Its basic statistical properties were derived and model parameters estimated using the method of maximum likelihood. The Proposed distribution was applied to Cancer Stem Cell data and compared to the Marshall Olkin Flexible Weibull Extension Distribution (MO-FWED), and the Marshall-Olkin exponential Weibull distribution (MO-EWD). The Marshall-Olkin Inverse Lomax distribution provided a better fit than the Marshall Olkin Flexible Weibull Extension Distribution, and the Marshall-Olkin exponential Weibull distribution based on log-likelihood AIC, CAIC, BIC and HQIC values.

scholarly journals Odd Lindley-Kumaraswamy Distribution: Model, Properties and Application

2020 ◽  
pp. 42-58
Author(s):  
Kuje Samson ◽  
Abubakar, Mohammad Auwal ◽  
Asongo, Iorkaa Abraham ◽  
Alhaji, Ismaila Sulaiman
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Distribution Model ◽  
Model Parameters ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Compound Distribution

This article uses the odd Lindley-G family of distributions to propose and study a new compound distribution called “odd Lindley-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lindley-Kumaraswamy distribution are defined and studied by deriving and discussing many properties of the distribution such as the ordinary moments, moment generating function, characteristics function, quantile function, reliability functions, order statistics and other useful measures. The unknown model parameters are also estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real life datasets. The results show that the proposed distribution outperforms the other fitted compound models selected for this study and hence it is a flexible generalization of the Kumaraswamy distribution.

scholarly journals Transmuted Modified Weibull distribution: Properties and Application

2018 ◽  
Vol 11 (2) ◽  
pp. 362-374
Author(s):  
Muhammad Shuaib Khan ◽  
Robert King ◽  
Irene L. Hudson
Keyword(s):  
Weibull Distribution ◽  
Survival Data ◽  
Model Parameters ◽  
Hazard Functions ◽  
Method Of Maximum Likelihood ◽  
The Mean ◽  
Moment Approach ◽  
Modified Weibull ◽  
Coefficient Of Skewness ◽  
Mean Variance

This research investigates the potential usefulness of the transmutedmodified Weibull distribution for modelling lifetime data. Weattain the diagnostic shapes of the density and hazard functions. Weformulate the expressions for the moments,incomplete moments, Renyientropy and q- entropy. We estimate the mean, variance, coefficientof variation, coefficient of skewness and coefficient of kurtosis basedon moment approach. The method of maximum likelihood is used forestimating the model parameters. We illustrate the use of transmutedmodified Weibull distribution with an application to survival data.

scholarly journals A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Pelumi E. Oguntunde ◽  
Mundher A. Khaleel ◽  
Mohammed T. Ahmed ◽  
Adebowale O. Adejumo ◽  
Oluwole A. Odetunmibi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Real Life ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Better Than

Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

scholarly journals The Transmuted Generalized Inverse Weibull Distribution

2014 ◽  
Vol 43 (2) ◽  
pp. 119-131 ◽  
Author(s):  
Faton Merovci ◽  
Ibrahim Elbatal ◽  
Alaa Ahmed
Keyword(s):  
Weibull Distribution ◽  
Generalized Inverse ◽  
Probability Distributions ◽  
Information Matrix ◽  
Real Data ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
Inverse Weibull Distribution

A generalization of the generalized inverse Weibull distribution the so-called transmuted generalized inverse Weibull distribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking the generalized inverseWeibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the flexibility of the transmuted version versus the generalized inverse Weibull distribution.

A Platform for Integrating and Sharing Cancer Stem Cell Data

2021 ◽  
Author(s):  
Irena Parvanova ◽  
Kirill Borziak ◽  
Jennifer Guarino ◽  
Joseph Finkelstein
Keyword(s):  
Stem Cell ◽  
Cancer Stem Cell ◽  
Cell Data

scholarly journals THE LOGISTIC INVERSE LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATIONS

2021 ◽  
Vol 09 (01) ◽  
Author(s):  
Ramesh Kumar Joshi ◽  
Keyword(s):  
Goodness Of Fit ◽  
Survival Function ◽  
Continuous Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution

In this article, a three-parameter continuous distribution is introduced called Logistic inverse Lomax distribution. We have discussed some mathematical and statistical properties of the distribution such as the probability density function, cumulative distribution function and hazard rate function, survival function, quantile function, the skewness, and kurtosis measures. The model parameters of the proposed distribution are estimated using three well-known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. The goodness of fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real data set.

scholarly journals The Beta Transmuted Weibull Distribution

2014 ◽  
Vol 43 (2) ◽  
pp. 133-149 ◽  
Author(s):  
Manisha Pal ◽  
Montip Tiensuwan
Keyword(s):  
Weibull Distribution ◽  
Censored Data ◽  
Weibull Model ◽  
Model Parameters ◽  
Lorenz Curves ◽  
Positive Data ◽  
Method Of Maximum Likelihood ◽  
Special Cases ◽  
The Mean ◽  
New Distribution

The paper introduces a beta transmuted Weibull distribution, which contains a number ofdistributions as special cases. The properties of the distribution are discussed and explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, and reliability. The distribution and moments of order statistics are also studied. Estimation of the model parameters by the method of maximum likelihood is discussed. The log beta transmuted Weibull model is introduced to analyze censored data. Finally, the usefulness of the new distribution in analyzing positive data is illustrated.

scholarly journals Alpha Power Transformed Inverse Lomax Distribution with Different Methods of Estimation and Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Ramadan A. ZeinEldin ◽  
Muhammad Ahsan ul Haq ◽  
Sharqa Hashmi ◽  
Mahmoud Elsehety
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Quantile Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Alpha Power ◽  
Lomax Distribution ◽  
Anderson Darling ◽  
Inverse Lomax Distribution

In this paper, a new three-parameter lifetime distribution, alpha power transformed inverse Lomax (APTIL) distribution, is proposed. The APTIL distribution is more flexible than inverse Lomax distribution. We derived some mathematical properties including moments, moment generating function, quantile function, mode, stress strength reliability, and order statistics. Characterization related to hazard rate function is also derived. The model parameters are estimated using eight estimation methods including maximum likelihood, least squares, weighted least squares, percentile, Cramer–von Mises, maximum product of spacing, Anderson–Darling, and right-tail Anderson–Darling. Numerical results are calculated to compare the performance of these estimation methods. Finally, we used three real-life datasets to show the flexibility of the APTIL distribution.

scholarly journals A new generalization of the inverse Lomax distribution with statistical properties and applications

2021 ◽  
Vol 8 (4) ◽  
pp. 89-97
Author(s):  
Hassan et al. ◽  
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Statistical Properties ◽  
Maximum Likelihood Estimates ◽  
Entropy Measure ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution ◽  
Mean Square Errors

In this paper, we introduce a new generalization of the inverse Lomax distribution with one extra shape parameter, the so-called power inverse Lomax (PIL) distribution, derived by using the power transformation method. We provide a more flexible density function with right-skewed, uni-modal, and reversed J-shapes. The new three-parameter lifetime distribution capable of modeling decreasing, Reversed-J and upside-down hazard rates shapes. Some statistical properties of the PIL distribution are explored, such as quantile measure, moments, moment generating function, incomplete moments, residual life function, and entropy measure. The estimation of the model parameters is discussed using maximum likelihood, least squares, and weighted least squares methods. A simulation study is carried out to compare the efficiencies of different methods of estimation. This study indicated that the maximum likelihood estimates are more efficient than the corresponding least squares and weighted least squares estimates in approximately most of the situations Also, the mean square errors for all estimates are decreasing as the sample size increases. Further, two real data applications are provided in order to examine the flexibility of the PIL model by comparing it with some known distributions. The PIL model offers a more flexible distribution for modeling lifetime data and provides better fits than other models such as inverse Lomax, inverse Weibull, and generalized inverse Weibull.

Cancer Stem Cell: A Big Hurdle in Cancer Therapy

2015 ◽  
Vol 1 (1) ◽  
pp. 1 ◽  
Author(s):  
Nahid Arghiani ◽  
Maryam M. Matin
Keyword(s):  
Stem Cell ◽  
Cancer Therapy ◽  
Cancer Stem Cell
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