Further theories on application of new generalized probability density function and its applications

Erem, Aysegul; Bilgehan, Bülent; Özyapıcı, Ali; Sensoy, Zehra Boratas

doi:10.1002/qre.3083

Cited by 2 publications

(1 citation statement)

References 25 publications

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“…Fundamentally, the likelihood function denotes the plausibility of data occurrences under varied parameter scenarios. Maximum likelihood estimation (MLE) represents an approach aimed at estimating model parameters by optimizing the likelihood function, thus seeking parameter values that optimize the probability of observed data occurrences within the selected statistical model [32]. Essentially, MLE fine-tunes parameter values to optimize the probability of observed data occurrences, resulting in the computed maximum likelihood estimate.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Clean Coal Ash Content in Coal Flotation through a Convergent Model Unifying Deep Learning and Likelihood Function, Incorporating Froth Velocity and Reagent Dosage Parameters

Lu,

Liu,

2023

Processes

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This study successfully achieved high-precision detection of the clean coal ash content in the coal froth flotation domain by integrating deep learning with the likelihood function. Methodologically, a novel data processing and prediction framework was established by combining a deep learning Keras neural network with the likelihood function from probability statistics. The SIFT algorithm was utilized to extract key feature points and descriptors from the images, and keypoint matching and mean-shift clustering algorithms were employed to accurately obtain information on foam motion trajectories and velocities. For parameter optimization, the maximum likelihood estimation was applied to find the optimal parameter estimates of the likelihood function, ensuring enhanced model accuracy. By incorporating the optimized likelihood function parameters into the Keras deep neural network, an efficient prediction model was constructed for the dosage of flotation reagents, froth velocity, and clean coal ash content. The model’s evaluation involved six performance metrics. The experimental results were highly significant, with R2 at 0.99997%, RMSE at 0.04458%, MAE at 0.00170%, MAPE at 0.02329%, RRSE at 0.00994%, and MAAPE at 0.00067%.

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Section: Introductionmentioning

confidence: 99%

Prediction of Clean Coal Ash Content in Coal Flotation through a Convergent Model Unifying Deep Learning and Likelihood Function, Incorporating Froth Velocity and Reagent Dosage Parameters

Lu,

Liu,

2023

Processes

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Survival Analysis of Type-II Lehmann Fréchet Parameters via Progressive Type-II Censoring with Applications

Elshahhat

Bhattacharya

Mohammed

2022

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A new three-parameter Type-II Lehmann Fréchet distribution (LFD-TII), as a reparameterized version of the Kumaraswamy–Fréchet distribution, is considered. In this study, using progressive Type-II censoring, different estimation methods of the LFD-TII parameters and its lifetime functions, namely, reliability and hazard functions, are considered. In a frequentist setup, both the likelihood and product of the spacing estimators of the considered parameters are obtained utilizing the Newton–Raphson method. From the normality property of the proposed classical estimators, based on Fisher’s information and the delta method, the asymptotic confidence interval for any unknown parametric function is obtained. In the Bayesian paradigm via likelihood and spacings functions, using independent gamma conjugate priors, the Bayes estimators of the unknown parameters are obtained against the squared-error and general-entropy loss functions. Since the proposed posterior distributions cannot be explicitly expressed, by combining two Markov-chain Monte-Carlo techniques, namely, the Gibbs and Metropolis–Hastings algorithms, the Bayes point/interval estimates are approximated. To examine the performance of the proposed estimation methodologies, extensive simulation experiments are conducted. In addition, based on several criteria, the optimum censoring plan is proposed. In real-life practice, to show the usefulness of the proposed estimators, two applications based on two different data sets taken from the engineering and physics fields are analyzed.

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Further theories on application of new generalized probability density function and its applications

Cited by 2 publications

References 25 publications

Prediction of Clean Coal Ash Content in Coal Flotation through a Convergent Model Unifying Deep Learning and Likelihood Function, Incorporating Froth Velocity and Reagent Dosage Parameters

Prediction of Clean Coal Ash Content in Coal Flotation through a Convergent Model Unifying Deep Learning and Likelihood Function, Incorporating Froth Velocity and Reagent Dosage Parameters

Survival Analysis of Type-II Lehmann Fréchet Parameters via Progressive Type-II Censoring with Applications

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