scholarly journals A New Extension of Quasi Lindley Distribution: Properties and Applications

2019 ◽  
Vol 7 (2) ◽  
pp. 28
Author(s):  
Patrick Udoudo Unyime ◽  
Ette Harrison Etuk
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Point Estimation ◽  
Maximum Likelihood Estimates ◽  
Lindley Distribution ◽  
Likelihood Point ◽  
Point Estimation Method ◽  
New Distribution

In this paper, we introduced and studied the statistical properties of a new distribution called the Marshall-Olkin extended quasi Lindley distribution. Specifically, we derived the crude moment, moment generating function, quantile function, and distributions of order statisticsbased on the distribution. The maximum likelihood point estimation method was used to estimate the parameters of the newly introduced model. Some AR minfication processes were discussed. We illustrated the applicability of the distribution using a real dataset.Keywords: Marshal-Olkin family of distributions; maximum likelihood estimates; minification processes; quasi Lindley distribution; quantile function.

scholarly journals A Comparative Study of Traditional and Kullback-Leibler Divergence of Survival Functions Estimators for the Parameter of Lindley Distribution

2019 ◽  
Vol 48 (5) ◽  
pp. 45-53 ◽  
Author(s):  
Sultan Parveen ◽  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Dinesh Kumar
Keyword(s):  
Maximum Likelihood ◽  
Comparative Study ◽  
Estimation Method ◽  
Point Estimation ◽  
Least Square ◽  
Simulation Studies ◽  
Survival Functions ◽  
Lindley Distribution ◽  
Leibler Divergence ◽  
Point Estimation Method

A new point estimation method based on Kullback-Leibler divergence of survival functions (KLS), measuring the distance between an empirical and prescribed survival functions, has been used to estimate the parameter of Lindley distribution. The simulation studies have been carried out to compare the performance of the proposed estimator with the corresponding Least square (LS), Maximum likelihood (ML) and Maximum product spacing (MPS) methods of estimation.

scholarly journals The Marshall-Olkin Extended Gumbel-weibull Distribution: Properties And Applications

2021 ◽  
Vol 16 (1) ◽  
pp. 2603-2627
Author(s):  
Elebe Emmanuel Nwezza ◽  
Fidelis Ifeanyi Ugwuowo
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Estimation Method ◽  
Quantile Function ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Simulation Studies ◽  
Test Statistics ◽  
Maximum Likeli ◽  
New Distribution

We introduce a new lifetime distribution called Marshall-Olkin extended Gumbel-Weibull. Some properties of distribution such as moments, TL-moments, quantile function, en- tropy, and order statistics are studied. The fexibility of the distribution to model unimodal, monotone shapes as well as unimodal, bimodal, monotone failure rates are presented. The estimators of the parameters of the distribution were obtained using the maximum likeli- hood estimation method. The performance of the maximum likelihood estimates of the Marshall-Olkin extended Gumbel-Weibulll parameters was observed through simulation studies. Two real life applications to illustrate the potentials of the new distribution are presented, and comparison with other distribution having the same baseline is done using goodness-of-test statistics.

scholarly journals The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application

2018 ◽  
pp. 1-17
Author(s):  
Mustapha Muhammad ◽  
Isyaku Muhammad ◽  
Aisha Muhammad Yaya
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Alternative Methods ◽  
Finite Sample ◽  
Modified Maximum Likelihood ◽  
Probability Weighted Moments

In this paper, a new lifetime model called Kumaraswamy exponentiated U-quadratic (KwEUq) distribution is proposed. Several mathematical and statistical properties are derived and studied such as the explicit form of the quantile function, moments, moment generating function, order statistics, probability weighted moments, Shannon entropy and Renyi entropy. We also found that the usual maximum likelihood estimates (MLEs) fail to hold for the KwEUq distribution. Two alternative methods are suggested for the parameter estimation of the KwEUq, the alternative maximum likelihood estimation (AMLE) and modified maximum likelihood estimation (MMLE). Simulation studies were conducted to assess the finite sample behavior of the AMLEs and MMLEs. Finally, we provide application of the KwEUq for illustration purposes.

scholarly journals A Four-Parameter Extension of Burr III Distribution with Applications

2021 ◽  
Vol 3 (1) ◽  
pp. 7-19
Author(s):  
Emmanuel W. Okereke ◽  
Johnson Ohakwe
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Linear Representation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Maximum Likelihood Procedure ◽  
Burr Iii Distribution ◽  
New Distribution

AbstractIn this paper, we defined and studied a new distribution called the odd exponentiated half-logistic Burr III distribution. Properties such as the linear representation of the probability density function (PDF) of the distribution, quantile function, ordinary and incomplete moments, moment generating function and distribution of the order statistic were derived. The PDF and hazard rate function were found to be capable of having various shapes, making the new distribution highly flexible. In particular, the hazard rate function can be nonincreasing, unimodal and nondecreasing. It can also have the bathtub shape among other non- monotone shapes. The maximum likelihood procedure was used to estimate the parameters of the new model. We gave two numerical examples to illustrate the usefulness and the ability of the distribution to provide better fits to a number of data sets than several distributions in existence.Keywords: Burr III distribution; maximum likelihood procedure; moments; odd exponentiated half-logistic-G family; order statistics. AbstrakPada artikel ini akan didefinisikan dan dipelajari mengenai distribusi baru yang disebut distribusi Burr III setengah logistik tereksponen ganjil. Kami menurunkan beberapa sifat dari distribusi tersebut yaitu representasi linier dari fungsi kepadatan peluang (FKP), fungsi kuantil, momen biasa dan momen tidak lengkap, fungsi pembangkit momen dan distribusi statistik terurut. Fungsi FKP dan fungsi tingkat hazard diperoleh memiliki bermacam-macam bentuk, membuat distribusi baru ini sangat fleksibel. Secara khusus, fungsi tingkat hazard dapat berupa fungsi taknaik, bermodus tunggal, bisa juga tidak turun. Selain itu, fungsi ini juga dapat berbentuk seperti bak mandi di antara bentuk-bentuk tak monoton lainnya. Prosedur kemungkinan maksimum digunakan untuk mengestimasi parameter model yang baru. Kami memberikan dua contoh numerik untuk mengilustrasikan kegunaan dan kemampuan distribusi untuk menghasilkan kesesuaian yang lebih baik pada sejumlah kumpulan data dibandingkan beberapa distribusi yang ada.Kata kunci: distribusi Burr III; prosedur kemungkinan maksimum; momen; keluarga setengah logistik-G teresponen ganjil; statistic terurut.

scholarly journals The Zubair-dagum Distribution

2021 ◽  
pp. 25-35
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Dagum Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals Allocation of EV Public Charging Station in Renewable based Distribution Network using HHO Considering Uncertainties and Traffic Congestion

2021 ◽  
Author(s):  
Arnab Pal ◽  
Aniruddha Bhattacharya ◽  
Ajoy Kumar Chakraborty
Keyword(s):  
Distribution System ◽  
Traffic Congestion ◽  
Distribution Network ◽  
Estimation Method ◽  
Point Estimation ◽  
Rank Test ◽  
Voltage Profile ◽  
Charging Station ◽  
Soft Computing Techniques ◽  
Point Estimation Method

Abstract Electric vehicle (EV) is the growing vehicular technology for sustainable development to reduce carbon emission and to save fossil fuel. The charging station (CS) is necessary at appropriate locations to facilitate the EV owners to charge their vehicle as well as to keep the distribution system parameters within permissible limits. Besides that, the selection of a charging station is also a significant task for the EV user to reduce battery energy wastage while reaching the EV charging station. This paper presents a realistic solution for the allocation of public fast-charging stations (PFCS) along with solar distributed generation (SDG). A 33 node radial distribution network is superimposed with the corresponding traffic network to allocate PFCSs and SDGs. Two interconnected stages of optimization are used in this work. The first part deals with the optimization of PFCS’s locations and SDG’s locations with sizes, to minimize the energy loss and to improve voltage profile using harris hawk optimization (HHO) and few other soft computing techniques. The second part handles the proper assignment of EVs to the PFCSs with less consumption of the EV’s energy considering the road distances with traffic congestion using linear programming (LP), where the shortest paths are decided by Dijkstra's algorithm. The 2m point estimation method (2m PEM) is employed to handle the uncertainties associated with EVs and SDGs. The robustness of solutions are tested using wilcoxon signed rank test and quade test.

scholarly journals Two-Stage Optimal Scheduling of Large-Scale Renewable Energy System Considering the Uncertainty of Generation and Load

2020 ◽  
Vol 10 (3) ◽  
pp. 971 ◽  
Author(s):  
Xiangyu Kong ◽  
Shuping Quan ◽  
Fangyuan Sun ◽  
Zhengguang Chen ◽  
Xingguo Wang ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Demand Response ◽  
Large Scale ◽  
Thermal Power ◽  
Estimation Method ◽  
Point Estimation ◽  
Low Carbon ◽  
System Operation ◽  
Two Stage ◽  
Point Estimation Method

With the development of smart grid and low-carbon electricity, a high proportion of renewable energy is connected to the grid. In addition, the peak-valley difference of system load increases, which makes the traditional grid scheduling method no longer suitable. Therefore, this paper proposes a two-stage low-carbon economic scheduling model considering the characteristics of wind, light, thermal power units, and demand response at different time scales. This model not only concerns the deep peak state of thermal power units under the condition of large-scale renewable energy, but also sets the uncertain models of PDR (Price-based Demand Response) virtual units and IDR (Incentive Demand Response) virtual units. Taking the system operation cost and carbon treatment cost as the target, the improved bat algorithm and 2PM (Two-point Estimation Method) are used to solve the problem. The introduction of climbing costs and low load operating costs can more truly reflect the increased cost of thermal power units. Meanwhile, the source-load interaction can weigh renewable energy limited costs and the increased costs of balancing volatility. The proposed method can be applied to optimal dispatch and safe operation analysis of the power grid with a high proportion of renewable energy. Compared with traditional methods, the total scheduling cost of the system can be reduced, and the rights and obligations of contributors to system operation can be guaranteed to the greatest extent.

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