scholarly journals Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

2017 ◽  
Vol 9 (4) ◽  
pp. 135
Author(s):  
Loai M. A. Al-Zou'bi
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Continuous Distribution ◽  
Quantile Function ◽  
Descriptive Statistics ◽  
Likelihood Method ◽  
Distribution Parameters ◽  
Rate Functions ◽  
Mean Variance ◽  
New Distribution

A new continuous distribution is proposed in this paper. This distribution is a generalization of Mukherjee-Islam distribution using the quadratic rank transmutation map. It is called transmuted Mukherjee-Islam distribution (TMID). We have studied many properties of the new distribution: Reliability and hazard rate functions. The descriptive statistics: mean, variance, skewness, kurtosis are also studied. Maximum likelihood method is used to estimate the distribution parameters. Order statistics and Renyi and Tsallis entropies were also calculated. Furthermore, the quantile function and the median are calculated.

scholarly journals Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1662
Author(s):  
Ahmed Sayed M. Metwally ◽  
Amal S. Hassan ◽  
Ehab M. Almetwally ◽  
B M Golam Kibria ◽  
Hisham M. Almongy
Keyword(s):  
Reliability Analysis ◽  
Confidence Intervals ◽  
Hazard Rate ◽  
Shape Parameter ◽  
Quantile Function ◽  
Proposed Model ◽  
Distribution Parameters ◽  
Rate Functions ◽  
New Distribution ◽  
Skewness And Kurtosis

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.

Truncated Cauchy Power Lomax Model and Its Application to Biomedical Data

2020 ◽  
Vol 12 (1) ◽  
pp. 16-24
Author(s):  
Abdullah M. Almarashi
Keyword(s):  
Maximum Likelihood Method ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Biomedical Data ◽  
Physical Sciences ◽  
Cancer Dataset ◽  
Fundamental Properties ◽  
New Distribution

In this study, we propose a new lifetime model, named truncated Cauchy power Lomax (TCPL) distribution. The TCPL distribution has many applications in biomedical and physical sciences, and we illustrate that its application herein. We used bladder cancer dataset related to medicine to illustrate the flexibility of the TCPL distribution. The new distribution is more flexible than some well-known models. We also calculated some fundamental properties like; moments, quantile function, moment generating function and order statistics for the TCPL model. The model parameters were estimated using maximum likelihood method for estimation. At the end of the paper, the simulation study is performed to assess the effectiveness of the estimates.

scholarly journals Truncated Akash distribution: properties and applications

2020 ◽  
Vol 9 (5) ◽  
pp. 179-184
Author(s):  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Coefficient Of Variation ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
Proposed Model ◽  
Rate Functions ◽  
Mean And Variance

In this paper, Truncated Akash distribution has been proposed. Its mean and variance have been derived. Nature of cumulative distribution and hazard rate functions have been derived and presented graphically. Its moments including Coefficient of Variation, Skenwness, Kurtosis and Index of dispersion have been derived. Maximum likelihood method of estimation has been used to estimate the parameter of proposed model. It has been applied on three data sets and compares its superiority over one parameter exponential, Lindley, Akash, Ishita and truncated Lindley distribution.

scholarly journals A New Extension of Lindley Geometric Distribution and its Applications

2019 ◽  
pp. 249-263
Author(s):  
I. Elbatal ◽  
Mohamed G. Khalil
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Geometric Distribution ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Distribution

A new four-parameter distribution called the beta Lindley-geometric distribution is proposed. The hazard rate function of the new model can be constant, decreasing, increasing, upside down bathtub or bathtub failure rate shapes. Various structural properties including of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated using a real data set.

scholarly journals Sine Half-Logistic Inverse Rayleigh Distribution: Properties, Estimation, and Applications in Biomedical Data

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. Shrahili ◽  
I. Elbatal ◽  
Mohammed Elgarhy
Keyword(s):  
Maximum Likelihood Method ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Biomedical Data ◽  
Type Ii ◽  
Entropy Measures ◽  
Distribution Parameters ◽  
Two Parameters

A new lifetime distribution with two parameters, known as the sine half-logistic inverse Rayleigh distribution, is proposed and studied as an extension of the half-logistic inverse Rayleigh model. The sine half-logistic inverse Rayleigh model is a new inverse Rayleigh distribution extension. In the application section, we show that the sine half-logistic inverse Rayleigh distribution is more flexible than the half-logistic inverse Rayleigh and inverse Rayleigh distributions. The statistical properties of the half-logistic inverse Rayleigh model are calculated, including the quantile function, moments, moment generating function, incomplete moment, and Lorenz and Bonferroni curves. Entropy measures such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, and Tsallis entropy are proposed for the sine half-logistic inverse Rayleigh distribution. To estimate the sine half-logistic inverse Rayleigh distribution parameters, statistical inference using the maximum likelihood method is used. Applications of the sine half-logistic inverse Rayleigh model to real datasets demonstrate the flexibility of the sine half-logistic inverse Rayleigh distribution by comparing it to well-known models such as half-logistic inverse Rayleigh, type II Topp–Leone inverse Rayleigh, transmuted inverse Rayleigh, and inverse Rayleigh distributions.

scholarly journals Inverted Beta Lindley Distribution

2017 ◽  
Vol 13 (1) ◽  
pp. 7074-7086
Author(s):  
Neveen Kilany ◽  
H M Atallah
Keyword(s):  
Method Of Moments ◽  
Maximum Likelihood Method ◽  
Information Matrix ◽  
Continuous Distribution ◽  
Real Data ◽  
Point Estimation ◽  
Likelihood Method ◽  
New Model ◽  
Positive Data ◽  
Rate Functions

In this paper, a three-parameter continuous distribution, namely, Inverted Beta-Lindley (IBL) distribution is proposed and studied. The new model turns out to be quite flexible for analyzing positive data and has various shapes of density and hazard rate functions. Several statistical properties associated with this distribution are derived. Moreover, point estimation via method of moments and maximum likelihood method are studied and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models.

scholarly journals Pseudo-Lindley Family of Distributions and its Properties

2021 ◽  
pp. 35-49
Author(s):  
U. U. Uwadi ◽  
E. E. Nwezza
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Quantile Function ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
New Family ◽  
The Family ◽  
Renyi’S Entropy ◽  
Family Of Distributions

In this study, we proposed a family of distribution called the Pseudo Lindley family of distributions. The limiting behaviors of the density and hazard rate function of the new family are examined. Statistical properties of the proposed family of distributions derived include quantile function, moments, order statistics, and Renyi’s entropy. The maximum likelihood method was employed in obtaining the parameter estimates of the Pseudo Lindley family of distribution. Bivariate extension of the proposed family is discussed. Some special members of the family are obtained. The shape of the density function of special members could be unimodal, bathtub shaped, increasing and decreasing. 

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

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