scholarly journals Statistical Inference of Odd Fréchet Inverse Lomax Distribution with Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Ramadan A. ZeinEldin ◽  
Muhammad Ahsan ul Haq ◽  
Sharqa Hashmi ◽  
Mahmoud Elsehety ◽  
M. Elgarhy
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Information Criterion ◽  
Value Theory ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Monte Carlo Simulation Study ◽  
Lifetime Distributions ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution

In this article, we propose and study a new three-parameter distribution, called the odd Fréchet inverse Lomax (OFIL) distribution, derived by combining the odd Fréchet-G family and the inverse Lomax distribution. Since Fréchet is a continuous distribution with wide applicability in extreme value theory, the new model contains these properties as well as the characteristics of the inverse Lomax distribution which make it more flexible and provide a good alternative for some well-known lifetime distributions. We initially present a linear representation of its functions and discussion on density and hazard rate function. Then, we study its various mathematical properties. Different estimation methods are used to estimate parameters of OFIL. The Monte Carlo simulation study is carried out to compare the efficiencies of different methods of estimation. The maximum likelihood estimation (MLE) method is used to estimate the OFIL parameters by considering three practical data applications. We show that the related model is the best in comparisons based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and other goodness-of-fit measures.

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 Modeling and Model Comparison for Industrial Production Index of Turkey, Brazil and G7 Countries

2018 ◽  
Vol 6 (04) ◽  
Author(s):  
Nihan Öksüz Narinç
Keyword(s):  
Industrial Production ◽  
Goodness Of Fit ◽  
Model Comparison ◽  
Information Criterion ◽  
Estimation Methods ◽  
Coefficient Of Determination ◽  
G7 Countries ◽  
Production Index ◽  
Industrial Production Index ◽  
Expected Values

In this study, it was aimed to modeling and model comparison for the industrial production index values of Turkey, Brazil and G7 countries among the years 1990-2017. The curve estimation methods (linear, quadratic, qubic, and hyperbolastic) and some non-linear time series models (Weibull, Negative Exponential, Brody, Gompertz, Logistic, Von Bertalanffy, Richards) were used for modeling the longitudinal data of monthly industrial production index values. The most fitted Gompertz model for all three data sets was determined according to the criteria of goodness of fit (coefficient of determination, mean square error, Akaike's information criterion, Bayesian information criterion), using the process between 1990-2008 (up to the 2008 crisis). After the 2008-2009 crisis, Brazil and G7 countries' industrial production index values were well below their expected values. In contrast, Turkey's expected values and the actual values for the industrial production index have been fairly close. Considering these results, it can be said that Turkey was less affected in terms of the effects of the 2008-2009 economic crisis than other countries. Industrial production index values of Turkey at 100th anniversary of the founding of the Republic of Turkey in 2023, and other important dates in 2041 and 2050 were estimated to be 177.62, 353.49 and 485.63, respectively.

scholarly journals An Inferential Aptness of a Weibull Generated Distribution and Application

2021 ◽  
Author(s):  
Brijesh P. Singh ◽  
Utpal Dhar Das
Keyword(s):  
Weibull Distribution ◽  
Continuous Distribution ◽  
Selection Criterion ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Single Parameter ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lifetime Distributions ◽  
Limiting Behavior

In this article an attempt has been made to develop a flexible single parameter continuous distribution using Weibull distribution. The Weibull distribution is most widely used lifetime distributions in both medical and engineering sectors. The exponential and Rayleigh distribution is particular case of Weibull distribution. Here in this study we use these two distributions for developing a new distribution. Important statistical properties of the proposed distribution is discussed such as moments, moment generating and characteristic function. Various entropy measures like Rényi, Shannon and cumulative entropy are also derived. The kthkt⁢h order statistics of pdf and cdf also obtained. The properties of hazard function and their limiting behavior is discussed. The maximum likelihood estimate of the parameter is obtained that is not in closed form, thus iteration procedure is used to obtain the estimate. Simulation study has been done for different sample size and MLE, MSE, Bias for the parameter λλ has been observed. Some real data sets are used to check the suitability of model over some other competent distributions for some data sets from medical and engineering science. In the tail area, the proposed model works better. Various model selection criterion such as -2LL, AIC, AICc, BIC, K-S and A-D test suggests that the proposed distribution perform better than other competent distributions and thus considered this as an alternative distribution. The proposed single parameter distribution is found more flexible as compare to some other two parameter complicated distributions for the data sets considered in the present study.

scholarly journals The ArcTan Lomax Distribution with Properties and Applications

2021 ◽  
pp. 117-125
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Survival Analysis ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
And Mathematics

Here, in this paper, a continuous distribution called ArcTan Lomax distribution with three-parameter has been introduced along with some relevant properties of statistics and mathematics pertaining to the distribution. With the help of three established estimations methods including maximum likelihood estimation (MLE), estimation of the presented distribution’s model parameters is done. Also with the help of a real set of data, the distribution’s goodness-of-fit is examined in contrast to some established models in survival analysis.

scholarly journals Weighted Power Lomax Distribution and its Length Biased Version: Properties and Estimation Based on Censored Samples

2021 ◽  
pp. 343-356
Author(s):  
Amal Soliman Hassan ◽  
Ehab M. Almetwally ◽  
Mundher Abdullah Khaleel ◽  
Heba Fathy Nagy
Keyword(s):  
Real Life ◽  
Model Parameters ◽  
Weighted Version ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Lifetime Distributions ◽  
Lomax Distribution ◽  
Censored Samples ◽  
Real Life Data ◽  
Asymptotic Confidence Intervals

In this paper, a weighted version of the power Lomax distribution referred to the weighted power Lomax distribution, is introduced. The new distribution comprises the length biased and the area biased of the power Lomax distribution as new models as well as containing an existing model as the length biased Lomax distribution as special model. Essential distributional properties of the weighted power Lomax distribution are studied. Maximum likelihood and maximum product spacing methods are proposed for estimating the population parameters in cases of complete and Type-II censored samples. Asymptotic confidence intervals of the model parameters are obtained. A sample generation algorithm along with a Monte Carlo simulation study is provided to demonstrate the pattern of the estimates for different sample sizes. Finally, a real-life data set is analyzed as an illustration and its length biased distribution is compared with some other lifetime distributions.

Comparison of Parametric Models: Appication to Hypertensive Patients in a Teaching Hospital, Awka

2020 ◽  
Author(s):  
Ibenegbu Amuche H ◽  
Osuji George A ◽  
Umeh Edith U
Keyword(s):  
Teaching Hospital ◽  
Standard Error ◽  
Goodness Of Fit ◽  
Information Criterion ◽  
Step Function ◽  
Parametric Models ◽  
University Teaching ◽  
Lifetime Distributions ◽  
Hypertensive Patients ◽  
Gompertz Distribution

Introduction: In Nigeria, hypertension is a common sickness among grownups. This research was carried out to determine the best model for predicting survival of hypertensive patients using goodness of fit criteria, Standard Error (SE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Method: A total of 105 patients who were diagnosed with hypertension from January 2013 to July 2018 were considered in which death is the event of interest. Six parametric models such as; exponential, Weibull, Lognormal, Log-logistic, Gompertz and hypertabastic distribution were fitted to the data using goodness of fit such as S.E, AIC and BIC to determine the best model. The parametric models were considered because they are all lifetime distributions. Results The result shows that the hypertabastic distribution has the lowest AIC and BIC, followed by Gompertz distribution. The standard error also indicates the hypertabastic model is better because it has the least value of standard error. This indicates that in terms of relative efficiency and parameterization the hypertabastic model is the best. The Survival Probability Plot of the six parametric models shows that the Hypertabastic distribution best fitted the data because it shows a clear step function than the other distribution and this justifies the result SE, AIC and BIC presented. Conclusion: Since hypertabastic distribution has the lowest SE, AIC and BIC it indicates that it is the best parametric model for predicting survival of hypertensive patients in chukwuemeka Odumegwu Ojukwu university teaching hospital Awka, Nigeria.

Frequency analysis of low flows using the Akaike information criterion

1996 ◽  
Vol 23 (6) ◽  
pp. 1180-1189 ◽  
Author(s):  
Semiu A. Lawal ◽  
W. Edgar Watt
Keyword(s):  
Lower Bound ◽  
Frequency Analysis ◽  
Akaike Information Criterion ◽  
Goodness Of Fit ◽  
Current Practice ◽  
Information Criterion ◽  
Low Flow ◽  
Parameter Distribution ◽  
Two Parameter ◽  
Parameter Distributions

It is the current practice in frequency analysis of low flows to consider only three-parameter distributions in which one of the parameters represents a nonzero lower bound. When applied to the small samples typically available, this practice results in incorrect low flow estimates. These errors are related to errors in the estimated lower bound. To preclude this possibility, it is proposed that the current practice be changed to include the selection of a two-parameter distribution in certain situations. To assess this proposal, the Akaike information criterion (AIC) is used to compare the suitability of the most commonly used three-parameter distribution (three-parameter Weibull) and three two-parameter distributions (two-parameter Weibull, Gumbel, and lognormal) to low flow data for 51 long-term hydrometric stations across Canada. For 75% of the stations, a two-parameter distribution is selected over the three-parameter distribution if the selection criterion is minimum AIC. In about one third of the remaining 25% of the stations where the three-parameter Weibull distribution gave the minimum AIC, the estimated lower bound is sufficiently close to the minimum observed low flow to indicate overfitting and hence unreliable quantile estimates. When the AIC is supplemented with visual examination of goodness of fit on probability plots, it is found that the lognormal distribution could very well fit those cases where the AIC selected the three-parameter Weibull distribution. Key words: low flow frequency, goodness of fit, information criterion, probability plot.

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 On the Accuracy of the Sine Power Lomax Model for Data Fitting

Modelling ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 78-104
Author(s):  
Vasili B. V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Statistical Model ◽  
Simulation Study ◽  
Statistical Models ◽  
Goodness Of Fit ◽  
Data Fitting ◽  
Applied Science ◽  
Survival Distribution ◽  
Lomax Distribution ◽  
Model Based

Every day, new data must be analysed as well as possible in all areas of applied science, which requires the development of attractive statistical models, that is to say adapted to the context, easy to use and efficient. In this article, we innovate in this direction by proposing a new statistical model based on the functionalities of the sinusoidal transformation and power Lomax distribution. We thus introduce a new three-parameter survival distribution called sine power Lomax distribution. In a first approach, we present it theoretically and provide some of its significant properties. Then the practicality, utility and flexibility of the sine power Lomax model are demonstrated through a comprehensive simulation study, and the analysis of nine real datasets mainly from medicine and engineering. Based on relevant goodness of fit criteria, it is shown that the sine power Lomax model has a better fit to some of the existing Lomax-like distributions.

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