scholarly journals Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications

2020 ◽  
Vol 25 (4) ◽  
pp. 65
Author(s):  
Jismi Mathew ◽  
Christophe Chesneau
Keyword(s):  
Stochastic Order ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Maxwell Distribution ◽  
Proposed Model ◽  
The Mean ◽  
The One ◽  
Mean Variance

It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall–Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall–Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills.

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 A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249001
Author(s):  
Ahtasham Gul ◽  
Muhammad Mohsin ◽  
Muhammad Adil ◽  
Mansoor Ali
Keyword(s):  
Hazard Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Model Parameters ◽  
Truncated Distribution ◽  
Unknown Parameters ◽  
Proposed Model

Truncated models are imperative to efficiently analyze the finite data that we observe in almost all the real life situations. In this paper, a new truncated distribution having four parameters named Weibull-Truncated Exponential Distribution (W-TEXPD) is developed. The proposed model can be used as an alternative to the Exponential, standard Weibull and shifted Gamma-Weibull and three parameter Weibull distributions. The statistical characteristics including cumulative distribution function, hazard function, cumulative hazard function, central moments, skewness, kurtosis, percentile and entropy of the proposed model are derived. The maximum likelihood estimation method is employed to evaluate the unknown parameters of the W-TEXPD. A simulation study is also carried out to assess the performance of the model parameters. The proposed probability distribution is fitted on five data sets from different fields to demonstrate its vast application. A comparison of the proposed model with some extant models is given to justify the performance of the W-TEXPD.

scholarly journals An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1815
Author(s):  
Diego I. Gallardo ◽  
Mário de Castro ◽  
Héctor W. Gómez
Keyword(s):  
Estimation Method ◽  
Selection Criterion ◽  
Likelihood Method ◽  
Simulation Studies ◽  
Cure Rate ◽  
Nested Models ◽  
Proposed Model ◽  
The Em Algorithm ◽  
Competing Causes ◽  
The One

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature.

scholarly journals Tropopause and jetlet characteristics in relation to thunderstorm development over Cyprus

2010 ◽  
Vol 23 ◽  
pp. 113-117
Author(s):  
A. Orphanou ◽  
K. Nicolaides ◽  
D. Charalambous ◽  
P. Lingis ◽  
S. C. Michaelides
Keyword(s):  
Wind Direction ◽  
The Other ◽  
Statistical Characteristics ◽  
Radiosonde Data ◽  
Data Sets ◽  
Other Hand ◽  
The One

Abstract. In the present study, the monthly statistical characteristics of jetlet and tropopause in relation to the development of thunderstorms over Cyprus are examined. For the needs of the study the 12:00 UTC radiosonde data obtained from the Athalassa station (33.4° E, 35.1° N) for an 11-year period, from 1997 till 2007, were employed. On the basis of this dataset, the height and the temperature of the tropopause, as well as the height, wind direction and speed of the jetlet were estimated. Additionally, the days in the above period with observed thunderstorms were selected and the aforementioned characteristics of the jetlet and tropopause were noted. The two data sets were subsequently contrasted in an attempt to identify possible relations between thunderstorm development, on the one hand, and tropopause and jetlet characteristics, on the other hand.

scholarly journals A New Extended Two-Parameter Distribution: Properties, Estimation Methods, and Applications in Medicine and Geology

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1578 ◽  
Author(s):  
Hazem Al-Mofleh ◽  
Ahmed Z. Afify ◽  
Noor Akma Ibrahim
Keyword(s):  
Estimation Method ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Proposed Model ◽  
Rate Functions ◽  
The Mean ◽  
Modeling Data ◽  
Two Parameter

In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall–Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson–Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

BHLM: Bayesian theory-based hybrid learning model for multi-document summarization

2018 ◽  
Vol 09 (02) ◽  
pp. 1850028
Author(s):  
S. Suneetha ◽  
A. Venugopal Reddy
Keyword(s):  
Hybrid Learning ◽  
Learning Model ◽  
Bayesian Theory ◽  
Probability Measures ◽  
Class Label ◽  
Document Summarization ◽  
Proposed Model ◽  
The Mean ◽  
Training Error ◽  
Mean Variance

In order to understand and organize the document in an efficient way, the multi-document summarization becomes the prominent technique in the Internet world. As the information available is in a large amount, it is necessary to summarize the document for obtaining the condensed information. To perform the multi-document summarization, a new Bayesian theory-based Hybrid Learning Model (BHLM) is proposed in this paper. Initially, the input documents are preprocessed, where the stop words are removed from the document. Then, the feature of the sentence is extracted to determine the sentence score for summarizing the document. The extracted feature is then fed into the hybrid learning model for learning. Subsequently, learning feature, training error and correlation coefficient are integrated with the Bayesian model to develop BHLM. Also, the proposed method is used to assign the class label assisted by the mean, variance and probability measures. Finally, based on the class label, the sentences are sorted out to generate the final summary of the multi-document. The experimental results are validated in MATLAB, and the performance is analyzed using the metrics, precision, recall, [Formula: see text]-measure and rouge-1. The proposed model attains 99.6% precision and 75% rouge-1 measure, which shows that the model can provide the final summary efficiently.

Variability and repeatability of olfactometric results of n-butanol, pig odour and a synthetic gas mixture

2004 ◽  
Vol 50 (4) ◽  
pp. 65-73 ◽  
Author(s):  
N. Defoer ◽  
H. Van Langenhove
Keyword(s):  
Synthetic Mixture ◽  
Gas Mixture ◽  
Mixture Ratio ◽  
Air Samples ◽  
Complete Dataset ◽  
Synthetic Gas ◽  
Pig Farms ◽  
The Mean ◽  
The One ◽  
Mean Variance

For the purposes of a research project for the Flemish authorities, olfactometric measurements were carried out at six closed pig farms and six fattener farms. The results of these olfactometric measurements were compared with the olfactometric results of n-butanol samples and samples of a synthetic gas mixture of ethanethiol, methylacetate and 2-propanol in nitrogen, both analysed on the same days as the air samples from the pig farms. The results of the n-butanol tests for all panellists showed that nobody was qualified according to the CEN criteria, and that, consequently, these criteria are rather stringent. Comparing the variability of the results for the three different odours showed that the mean and standard deviation of the mean variance were not significantly different for the three odour types, which means that the repeatability of the panellist results was equal for the examined odour types. The principle of traceability was checked by comparing the variance of the n-butanol, pig odour and synthetic mixture ratio. For the complete dataset, the principle of traceability could not been proven for n-butanol. For the restricted dataset, the principle of traceability was more valid for n-butanol than for the mixture, but differences were small. Finally, normalization was looked for with regard to olfactometric measurements of air samples from pig farms based either on n-butanol or on the synthetic mixture. Both models had low determination coefficients, but the model based on the synthetic mixture gave better results than the one based on n-butanol.

scholarly journals comparison of methods for the estimation of Weibull distribution parameters

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Felix Nwobi ◽  
Chukwudi Ugomma
Keyword(s):  
Weibull Distribution ◽  
Stock Prices ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Goodness Of Fit Tests ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Maximum Likelihood Estimation Method

In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

scholarly journals A Continuous Blood Pressure Estimation Method Using Photoplethysmography by GRNN-Based Model

Sensors ◽  
2021 ◽  
Vol 21 (21) ◽  
pp. 7207
Author(s):  
Zheming Li ◽  
Wei He
Keyword(s):  
Blood Pressure ◽  
Estimation Method ◽  
Absolute Error ◽  
Disease Diagnosis ◽  
Generalized Regression Neural Network ◽  
British Hypertension Society ◽  
Proposed Model ◽  
The Mean ◽  
Blood Pressure Estimation ◽  
The Time Domain

Compared with diastolic blood pressure (DBP) and systolic blood pressure (SBP), the blood pressure (BP) waveform contains richer physiological information that can be used for disease diagnosis. However, most models based on photoplethysmogram (PPG) signals can only estimate SBP and DBP and are susceptible to noise signals. We focus on estimating the BP waveform rather than discrete BP values. We propose a model based on a generalized regression neural network to estimate the BP waveform, SBP and DBP. This model takes the raw PPG signal as input and BP waveform as output. The SBP and DBP are extracted from the estimated BP waveform. In addition, the model contains encoders and decoders, and their role is to be responsible for the conversion between the time domain and frequency domain of the waveform. The prediction results of our model show that the mean absolute error is 3.96 ± 5.36 mmHg for SBP and 2.39 ± 3.28 mmHg for DBP, the root mean square error is 5.54 for SBP and 3.45 for DBP. These results fulfill the Association for the Advancement of Medical Instrumentation (AAMI) standard and obtain grade A according to the British Hypertension Society (BHS) standard. The results show that the proposed model can effectively estimate the BP waveform only using the raw PPG signal.

scholarly journals An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

2021 ◽  
Vol 17 (2) ◽  
pp. 59-74
Author(s):  
S. Qurat Ul Ain ◽  
K. Ul Islam Rather
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Statistical Properties ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean Variance ◽  
New Distribution ◽  
Extra Parameter

Abstract In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

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