scholarly journals The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2277
Author(s):  
Mahmoud El-Morshedy ◽  
Hassan M. Aljohani ◽  
Mohamed S. Eliwa ◽  
Mazen Nassar ◽  
Mohammed K. Shakhatreh ◽  
...  
Keyword(s):  
Hazard Rate ◽  
Real Life ◽  
Real Data ◽  
Rate Function ◽  
Discrete Analog ◽  
Discrete Distributions ◽  
Discrete Version ◽  
Continuous Version ◽  
Data Set ◽  
Accelerated Life Tests

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model.

scholarly journals THE BETA-WEIBULL DISTRIBUTION ON THE LATTICE OF INTEGERS

2016 ◽  
Vol 39 (1) ◽  
pp. 40 ◽  
Author(s):  
Vahid Nekoukhou ◽  
Hamid Bidram ◽  
Rasool Roozegar
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Discrete Analog ◽  
Discrete Distributions ◽  
Hazard Rate Function ◽  
Data Set ◽  
Beta Weibull Distribution ◽  
New Distribution

In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contains several discrete distributions as special sub-models. Some distributional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined.

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 Discretization of the method of generating an expanded family of distributions based upon truncated distributions

2021 ◽  
Vol 25 (Spec. issue 1) ◽  
pp. 19-30
Author(s):  
Muhammad Farooq ◽  
Muhammad Mohsin ◽  
Muhammad Naeem ◽  
Muhammad Farman ◽  
Ali Akgul ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Survival Function ◽  
Real Data ◽  
Reliability Function ◽  
Continuous Functions ◽  
Discrete Distributions ◽  
Discrete Version ◽  
Model Parameters ◽  
Data Set ◽  
Family Of Distributions

Discretization translates the continuous functions into discrete version making them more adaptable for numerical computation and application in applied mathematics and computer sciences. In this article, discrete analogues of a generalization method of generating a new family of distributions is provided. Several new discrete distributions are derived using the proposed methodology. A discrete Weibull-Geometric distribution is considered and various of its significant characteristics including moment, survival function, reliability function, quantile function, and order statistics are discussed. The method of maximum likelihood and the method of moments are used to estimate the model parameters. The performance of the proposed model is probed through a real data set. A comparison of our model with some existing models is also given to demonstrate its efficiency.

scholarly journals A New Generating Family of Distributions: Properties and Applications to the Weibull Exponential Model

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
El-Sayed A. El-Sherpieny ◽  
Salwa Assar ◽  
Tamer Helal
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Exponential Model ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Set ◽  
Rate Functions ◽  
Family Of Distributions

A new method for generating family of distributions was proposed. Some fundamental properties of the new proposed family include the quantile, survival function, hazard rate function, reversed hazard and cumulative hazard rate functions are provided. This family contains several new models as sub models, such as the Weibull exponential model which was defined and discussed its properties. The maximum likelihood method of estimation is using to estimate the model parameters of the new proposed family. The flexibility and the importance of the Weibull-exponential model is assessed by applying it to a real data set and comparing it with other known models.

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

REDEFINING FAILURE RATE FUNCTION FOR DISCRETE DISTRIBUTIONS

2002 ◽  
Vol 09 (03) ◽  
pp. 275-285 ◽  
Author(s):  
M. XIE ◽  
O. GAUDOIN ◽  
C. BRACQUEMOND
Keyword(s):  
Failure Rate ◽  
Rate Function ◽  
Monotonicity Property ◽  
Discrete Distributions ◽  
The Other ◽  
Continuous Case ◽  
Discrete Version ◽  
Series System ◽  
Failure Rate Function ◽  
Definition Of

For discrete distribution with reliability function R(k), k = 1, 2,…,[R(k - 1) - R(k)]/R(k - 1) has been used as the definition of the failure rate function in the literature. However, this is different from that of the continuous case. This discrete version has the interpretation of a probability while it is known that a failure rate is not a probability in the continuous case. This discrete failure rate is bounded, and hence cannot be convex, e.g., it cannot grow linearly. It is not additive for series system while the additivity for series system is a common understanding in practice. In the paper, another definition of discrete failure rate function as In[R(k - 1)/R(k)] is introduced, and the above-mentioned problems are resolved. On the other hand, it is shown that the two failure rate definitions have the same monotonicity property. That is, if one is increasing/decreasing, the other is also increasing/decreasing. For other aging concepts, the new failure rate definition is more appropriate. The failure rate functions according to this definition are given for a number of useful discrete reliability functions.

scholarly journals A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 603
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Abdul Hadi N. Ahmed ◽  
Ahmed Z. Afify
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Real Data ◽  
Moment Generating Function ◽  
Discrete Analog ◽  
Bias Reduction ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Probability Mass Function ◽  
Lindley Distribution

In this paper, we propose and study a new probability mass function by creating a natural discrete analog to the continuous Lindley distribution as a mixture of geometric and negative binomial distributions. The new distribution has many interesting properties that make it superior to many other discrete distributions, particularly in analyzing over-dispersed count data. Several statistical properties of the introduced distribution have been established including moments and moment generating function, residual moments, characterization, entropy, estimation of the parameter by the maximum likelihood method. A bias reduction method is applied to the derived estimator; its existence and uniqueness are discussed. Applications of the goodness of fit of the proposed distribution have been examined and compared with other discrete distributions using three real data sets from biological sciences.

Bayesian Structural Time Series

2020 ◽  
Vol 12 (1) ◽  
pp. 54-61
Author(s):  
Abdullah M. Almarashi ◽  
Khushnoor Khan
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Predictive Accuracy ◽  
Local Level ◽  
Real Life ◽  
Secondary Data ◽  
Real Data ◽  
Data Set ◽  
Structural Time Series ◽  
Structural Time

The current study focused on modeling times series using Bayesian Structural Time Series technique (BSTS) on a univariate data-set. Real-life secondary data from stock prices for flying cement covering a period of one year was used for analysis. Statistical results were based on simulation procedures using Kalman filter and Monte Carlo Markov Chain (MCMC). Though the current study involved stock prices data, the same approach can be applied to complex engineering process involving lead times. Results from the current study were compared with classical Autoregressive Integrated Moving Average (ARIMA) technique. For working out the Bayesian posterior sampling distributions BSTS package run with R software was used. Four BSTS models were used on a real data set to demonstrate the working of BSTS technique. The predictive accuracy for competing models was assessed using Forecasts plots and Mean Absolute Percent Error (MAPE). An easyto-follow approach was adopted so that both academicians and practitioners can easily replicate the mechanism. Findings from the study revealed that, for short-term forecasting, both ARIMA and BSTS are equally good but for long term forecasting, BSTS with local level is the most plausible option.

scholarly journals Discovery of Knowledge by using Data Warehousing as well as ETL Processing

2019 ◽  
Vol 8 (2S6) ◽  
pp. 936-945
Keyword(s):  
Data Warehouse ◽  
Real Life ◽  
Real Data ◽  
Automated Testing ◽  
Quality Of Data ◽  
Data Set ◽  
The Real ◽  
Using Data ◽  
Data Warehouse Quality

Testing is very essential in Data warehouse systems for decision making because the accuracy, validation and correctness of data depends on it. By looking to the characteristics and complexity of iData iwarehouse, iin ithis ipaper, iwe ihave itried ito ishow the scope of automated testing in assuring ibest data iwarehouse isolutions. Firstly, we developed a data set generator for creating synthetic but near to real data; then in isynthesized idata, with ithe help of hand icoded Extraction, Transformation and Loading (ETL) routine, anomalies are classified. For the quality assurance of data for a Data warehouse and to give the idea of how important the iExtraction, iTransformation iand iLoading iis, some very important test cases were identified. After that, to ensure the quality of data, the procedures of automated testing iwere iembedded iin ihand icoded iETL iroutine. Statistical analysis was done and it revealed a big enhancement in the quality of data with the procedures of automated testing. It enhances the fact that automated testing gives promising results in the data warehouse quality. For effective and easy maintenance of distributed data,a novel architecture was proposed. Although the desired result of this research is achieved successfully and the objectives are promising, but still there's a need to validate the results with the real life environment, as this research was done in simulated environment, which may not always give the desired results in real life environment. Hence, the overall potential of the proposed architecture can be seen until it is deployed to manage the real data which is distributed globally.

scholarly journals The partly parametric and partly nonparametric additive risk model

2021 ◽  
Author(s):  
Nils Lid Hjort ◽  
Emil Aas Stoltenberg
Keyword(s):  
Hazard Rate ◽  
Goodness Of Fit ◽  
Risk Model ◽  
Real Data ◽  
Rate Function ◽  
Nonparametric Model ◽  
Additive Risk Model ◽  
Data Application ◽  
Additive Risk ◽  
Hazard Factor

AbstractAalen’s linear hazard rate regression model is a useful and increasingly popular alternative to Cox’ multiplicative hazard rate model. It postulates that an individual has hazard rate function $$h(s)=z_1\alpha _1(s)+\cdots +z_r\alpha _r(s)$$ h ( s ) = z 1 α 1 ( s ) + ⋯ + z r α r ( s ) in terms of his covariate values $$z_1,\ldots ,z_r$$ z 1 , … , z r . These are typically levels of various hazard factors, and may also be time-dependent. The hazard factor functions $$\alpha _j(s)$$ α j ( s ) are the parameters of the model and are estimated from data. This is traditionally accomplished in a fully nonparametric way. This paper develops methodology for estimating the hazard factor functions when some of them are modelled parametrically while the others are left unspecified. Large-sample results are reached inside this partly parametric, partly nonparametric framework, which also enables us to assess the goodness of fit of the model’s parametric components. In addition, these results are used to pinpoint how much precision is gained, using the parametric-nonparametric model, over the standard nonparametric method. A real-data application is included, along with a brief simulation study.

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