Maximum Likelihood Approach Research Articles

Cytomegalovirus Infection in Pregnancy Prevention and Treatment Options: A Systematic Review and Meta-Analysis.

Cytomegalovirus (CMV) infection is a significant health concern affecting numerous expectant mothers across the globe. CMV is the leading cause of health problems and developmental delays among infected infants. Notably, this study examines CMV infection in pregnancy, its management, prevention mechanisms, and treatment options. Specifically, information from the Cochrane Library, PUBMED, Wiley Online, Science Direct, and Taylor Francis databases were reviewed along with additional records identified through the register, the Google Scholar search engine. Based on the search, 21 articles were identified for systematic review. A total of six randomized controlled trials (RCTs) were utilized for a meta-analytic review. As heterogeneity was substantial, the random effects model was used for meta-analysis. Utilizing the random-effects model, the restricted maximum likelihood (REML) approach, the estimate of effect size (d = -0.479, 95% CI = -0.977 to 0.019, p = 0.060) suggests the results are not statistically significant, so it cannot be inferred that the prevention methods used were effective, despite an inverse relationship between treatment and number of infected cases. The findings indicated that several techniques are used to prevent, diagnose, and manage CMV infection during pregnancy, including proper hygiene, ultrasound examination (US), magnetic resonance imaging (MRI), amniocentesis, viremia, hyperimmunoglobulin (HIG), and valacyclovir (VACV). The current review has significant implications for addressing CMV infection in pregnancy. Specifically, it provides valuable findings on contemporary management interventions to prevent and treat CMV infection among expectant mothers. Therefore, it allows relevant stakeholders to address these critical health concerns and understand the effectiveness of the proposed prevention and treatment options.

How to cross the desert if you are small and need mountains? Out‐of‐Ethiopia dispersal in Afromontane shrews

AbstractAimThe Eastern Afromontane Biodiversity Hotspot (EABH) offers an ideal location to investigate the evolutionary mechanisms producing a high level of endemic biodiversity. We tested the hypothesis that the cradle of Eastern Afromontane diversity is in the largest sub‐region of the EABH montane archipelago, that is the Ethiopian Highlands. Further, we expected that climate oscillations followed by elevational shifts in montane habitats facilitated the dispersal of small mammal populations across unsuitable arid lowlands.LocationMountains and highlands of East Africa.TaxonShrews of the genus Crocidura (Eastern Afromontane phylogenetic clade).MethodsWe collected comprehensive genetic data from 511 (mitochondrial gene for cytochrome b) and 147 (double digest Restriction‐Associated DNA sequencing) samples of Crocidura shrews across the EABH. We estimated phylogenetic relationships with Bayesian and Maximum Likelihood approaches. Population genetic analyses were performed in STRUCTURE to evaluate the internal structure of species outside Ethiopia. Ancestral area and dispersal routes were analysed by the BioGeoBears package.ResultsSix major phylogenomic clades were delimited based on concatenated nuclear loci. The mitochondrial phylogeny roughly matches nuclear phylogenies, but with poorer resolution. Five of the six revealed clades are restricted to the Ethiopian Highlands, which is unambiguously the cradle of the diversity of this group of mammals (also confirmed by the biogeographic analysis). All non‐Ethiopian and a single Ethiopian species fall into the sixth clade with poorly resolved internal relationships. Detailed population genetic analysis of SNP data revealed a pronounced structure with multiple gene pools in this clade; however, this structure only partly corresponds with the current taxonomy.Main ConclusionsEastern Afromontane Crocidura shrews originated in the Ethiopian Highlands. They radiated there, and through a single southward dispersal event across the Turkana depression, they colonised the rest of the EABH in response to diverse geomorphology and climatic changes during the Plio‐Pleistocene.

Adaptive Type-II Hybrid Progressive Censoring Samples for Statistical Inference of Comparative Inverse Weibull Distributions

Recently, there has been a lot of interest in comparative life testing for items under jointly censored schemes for products from multiple production lines. The inverse Weibull distribution (IWD) is commonly used in life testing and reliability theory. In this paper, we address the problem of statistical inference from comparative inverse Weibull distributions under joint samples. An adaptive type-II hybrid progressive censoring scheme (HPCS) is used to save the balance between the ideal test time and the number of observed failures. Under the adaptive type-II HPCS, unknown parameters of the inverse Weibull populations are estimated using both maximum likelihood and Bayesian approaches. Asymptotic confidence intervals are established using the observed Fisher information matrix and bootstrap confidence intervals. We suggest using Markov chain Monte Carlo (MCMC) techniques to compute credible intervals under independent gamma priors. Using Monte Carlo simulations, all theoretical conclusions are tested and contrasted. For illustration purposes, an actual sample from comparative populations is analysed.

Conditional likelihood inference in a heteroscedastic functional measurement error model

In this paper, we deal with inference about the structural parameters in a heteroscedastic functional measurement error models under the normal distribution assumption. Given a minimal sufficient statistic for the incidental parameters, the conditional maximum likelihood (CML) approach is used. We show that CML estimators have explicit expressions and their sampling distribution is exact. We also show that the classical test statistics to test hypotheses of interest coincide and have exact distributions. We apply the statistical inference tools developed to a data set on comparison of measurement methods.

Quantitative Associations between Season, Month, and Temperature-Humidity Index with Milk Yield, Composition, Somatic Cell Counts, and Microbial Load: A Comprehensive Study across Ten Dairy Farms over an Annual Cycle.

This current study addresses the knowledge gap regarding the influence of seasons, months, and THI on milk yield, composition, somatic cell counts (SCC), and total bacterial counts (TBC) of dairy farms in northeastern regions of Iran. For this purpose, ten dairy herds were randomly chosen, and daily milk production records were obtained. Milk samples were systematically collected from individual herds upon delivery to the dairy processing facility for subsequent analysis, including fat, protein, solids-not-fat (SNF), pH, SCC, and TBC. The effects of seasons, months, and THI on milk yield, composition, SCC, and TBC were assessed using an analysis of variance. To account for these effects, a mixed-effects model was utilized with a restricted maximum likelihood approach, treating month and THI as fixed factors. Our investigation revealed noteworthy correlations between key milk parameters and seasonal, monthly, and THI variations. Winter showed the highest milk yield, fat, protein, SNF, and pH (p < 0.01), whereas both SCC and TBC reached their lowest values in winter (p < 0.01). The highest values for milk yield, fat, and pH were recorded in January (p < 0.01), while the highest protein and SNF levels were observed in March (p < 0.01). December marked the lowest SCC and TBC values (p < 0.01). Across the THI spectrum, spanning from -3.6 to 37.7, distinct trends were evident. Quadratic regression models accounted for 34.59%, 21.33%, 4.78%, 20.22%, 1.34%, 15.42%, and 13.16% of the variance in milk yield, fat, protein, SNF, pH, SCC, and TBC, respectively. In conclusion, our findings underscore the significant impact of THI on milk production, composition, SCC, and TBC, offering valuable insights for dairy management strategies. In the face of persistent challenges posed by climate change, these results provide crucial guidance for enhancing production efficiency and upholding milk quality standards.

Model-based clustering of multipath propagation in powerline communication channels

Powerline communication (PLC) channels are known to exhibit multipath propagation behaviour. The authors present a model-based framework to address the challenge of clustering multipath propagation components (MPCs) in PLC channels for indoor low-voltage (LV) environments. The framework employs a range of finite-mixture models (FMMs), including the gamma mixture model, the inverse gamma mixture model, the Gaussian mixture model, the inverse Gaussian mixture model, the Nakagami mixture model, the inverse Nakagami mixture model (INMM) and the Rayleigh mixture model, to identify clusters of MPCs. A measurement campaign of an unknown indoor LV PLC channel is conducted to obtain a channel response. From the channel response, the delay and magnitude parameters of the MPCs are extracted using the space-alternating generalised expectation maximisation algorithm adopted only for these parameters. A maximum likelihood approach and the expectation–maximisation algorithm are employed to fit the FMMs to the MPC delay-magnitude dataset to cluster MPCs in the delay domain. The results of the model-fitting process are then evaluated using the corrected Akaike information criterion (AICc), which enables a fair comparison of the candidate models over the feasible and finite range of clusters. A novel algorithm is introduced for estimating the feasible and finite range of clusters using the extracted delay and magnitude MPC parameters. The AICc’s ranking results show that the INMM model provides the best fit. Davies–Bouldin (DB) and Calinski–Harabasz (CH) indexes are used to compare the model-based clustering approach to the conventional distance-based clustering methods. Validation results show that CH and DB indexes closely agree in the optimal number of MPC clusters for model-based clustering, which corresponds to the most within-cluster compactness of MPCs and to the most between-cluster separation in the delay domain.

A new extension of linear failure rate distribution with estimation, simulation, and applications

In this article, we provide a new three-parameter model derived from the newly reduced Cauchy power-G family and linked to the linear failure rate model. The truncated Cauchy power linear failure rate (TCPLFR) is the name given to this distribution. The TCPLFR distribution also contains the truncated Cauchy power Rayleigh distribution and the truncated Cauchy power exponential distribution as sub-models. The TCPLFR distribution has rising, falling, and U-shaped hazard rate functions. The distribution characteristics of the TCPLFR are presented. To compute the population parameters’ point and estimated confidence intervals, the maximum likelihood approach is employed. We explore the behavior of the maximum likelihood estimates as well as the estimated confidence intervals for the model parameters using Monte Carlo simulation. To demonstrate the significance and flexibility of the TCPLFR distribution, the Akaike information criterion (D1), Bayesian information criterion (D2), consistent Akaike information criterion (D3), Hannan–Quinn information criterion (D4), and Kolmogorov–Smirnov (D5) statistic with its p-value (D6) were employed. According to a real-world data analysis, the truncated Cauchy power linear failure rate distribution outperforms alternative models with two, three, and four parameters.

Image Segmentation of the Sudd Wetlands in South Sudan for Environmental Analytics by GRASS GIS Scripts

This paper presents the object detection algorithms GRASS GIS applied for Landsat 8-9 OLI/TIRS data. The study area includes the Sudd wetlands located in South Sudan. This study describes a programming method for the automated processing of satellite images for environmental analytics, applying the scripting algorithms of GRASS GIS. This study documents how the land cover changed and developed over time in South Sudan with varying climate and environmental settings, indicating the variations in landscape patterns. A set of modules was used to process satellite images by scripting language. It streamlines the geospatial processing tasks. The functionality of the modules of GRASS GIS to image processing is called within scripts as subprocesses which automate operations. The cutting-edge tools of GRASS GIS present a cost-effective solution to remote sensing data modelling and analysis. This is based on the discrimination of the spectral reflectance of pixels on the raster scenes. Scripting algorithms of remote sensing data processing based on the GRASS GIS syntax are run from the terminal, enabling to pass commands to the module. This ensures the automation and high speed of image processing. The algorithm challenge is that landscape patterns differ substantially, and there are nonlinear dynamics in land cover types due to environmental factors and climate effects. Time series analysis of several multispectral images demonstrated changes in land cover types over the study area of the Sudd, South Sudan affected by environmental degradation of landscapes. The map is generated for each Landsat image from 2015 to 2023 using 481 maximum-likelihood discriminant analysis approaches of classification. The methodology includes image segmentation by ‘i.segment’ module, image clustering and classification by ‘i.cluster’ and ‘i.maxlike’ modules, accuracy assessment by ‘r.kappa’ module, and computing NDVI and cartographic mapping implemented using GRASS GIS. The benefits of object detection techniques for image analysis are demonstrated with the reported effects of various threshold levels of segmentation. The segmentation was performed 371 times with 90% of the threshold and minsize = 5; the process was converged in 37 to 41 iterations. The following segments are defined for images: 4515 for 2015, 4813 for 2016, 4114 for 2017, 5090 for 2018, 6021 for 2019, 3187 for 2020, 2445 for 2022, and 5181 for 2023. The percent convergence is 98% for the processed images. Detecting variations in land cover patterns is possible using spaceborne datasets and advanced applications of scripting algorithms. The implications of cartographic approach for environmental landscape analysis are discussed. The algorithm for image processing is based on a set of GRASS GIS wrapper functions for automated image classification.

Deciphering Millet Diversity: Proteomic Clusters and Phylogenetic Insights

Deciphering Millet Diversity: Proteomic Clusters and Phylogenetic Insights

Maximum Gaussianality training for deep speaker vector normalization

Automatic Speaker Verification (ASV) is a critical task in pattern recognition and has been applied to various security-sensitive scenarios. The current state-of-the-art technique for ASV is based on deep embedding. However, a significant challenge with this approach is that the resulting deep speaker vectors tend to be irregularly distributed. To address this issue, this paper proposes a novel training method called Maximum Gaussianality (MG), which regulates the distribution of the speaker vectors. Compared to the conventional normalization approach based on maximum likelihood (ML), the new approach directly maximizes the Gaussianality of the latent codes, and therefore can both normalize the between-class and within-class distributions in a controlled and reliable way and eliminate the unbound likelihood problem associated with the conventional ML approach. Our experiments on several datasets demonstrate that our MG-based normalization can deliver much better performance than the baseline systems without normalization and outperform discriminative normalization flow (DNF), an ML-based normalization method, particularly when the training data is limited. In theory, the MG criterion can be applied to any task in any research domain where Gaussian distributions are needed, making the MG training a versatile tool.

Assessment of positive selection across SARS-CoV-2 variants via maximum likelihood.

Study of the genome of the SARS-CoV-2 virus, particularly with regard to understanding evolution of the virus, is crucial for managing the COVID-19 pandemic. To this end, we sample viral genomes from the GISAID repository and use several of the maximum likelihood approaches implemented in PAML, a collection of open source programs for phylogenetic analyses of DNA and protein sequences, to assess evidence for positive selection in the protein-coding regions of the SARS-CoV-2 genome. Across all major variants identified by June 2021, we find limited evidence for positive selection. In particular, we identify positive selection in a small proportion of sites (5-15%) in the protein-coding region of the spike protein across variants. Most other variants did not show a strong signal for positive selection overall, though there were indications of positive selection in the Delta and Kappa variants for the nucleocapsid protein. We additionally use a forward selection procedure to fit a model that allows branch-specific estimates of selection along a phylogeny relating the variants, and find that there is variation in the selective pressure across variants for the spike protein. Our results highlight the utility of computational approaches for identifying genomic regions under selection.

Phylogeny and morphological evolution of the Neotropical genus Cuspidaria (Bignonieae, Bignoniaceae): Combining high‐throughput sequencing and targeted loci data

AbstractThe combined use of high‐throughput sequencing (HTS) with targeted loci data offers an excellent opportunity to reconstruct robust and comprehensive phylogenies at fine taxonomic scales using a hybrid approach. In this study, we infer the phylogeny of Cuspidaria (Bignonieae, Bignoniaceae), a diverse clade of lianas and shrubs centered in South America's wet and dry forests. We used HTS to obtain complete or nearly complete plastome sequences of seven individuals of Cuspidaria selected to represent the main clades in the genus. This sampling strategy aimed to reconstruct relationships at deeper nodes (i.e., backbone). We also used targeted loci data obtained through Sanger sequencing to obtain sequences of two chloroplast markers (ndhF, rpl32‐trnL) and one nuclear marker (PepC) for multiple individuals of 18 out of the 21 species of Cuspidaria recognized in the most recent treatment of the genus; only C. emmonsii, C. lachnaea, and C. simplicifolia were not sampled. This broad sampling strategy aimed to test the monophyly of individual species and reconstruct fine‐scale interspecific relationships within the genus. Both datasets were analyzed separately and combined using Bayesian inference and maximum likelihood approaches. The combined dataset includes 65 individuals representing 18 previously recognized species of Cuspidaria plus outgroup taxa. The analysis of the combined dataset recovered a monophyletic Cuspidaria, excluding C. bracteata, which was nested within the outgroup and is best treated elsewhere. Ancestral character state reconstructions provided novel insights into the evolution of morphology and identified multiple putative morphological synapomorphies for key lineages of Cuspidaria. Namely, anthers curved forward was reconstructed as a potential synapomorphy for the Cuspidaria clade, whereas interpetiolar gland fields in stems and inflorescence, subulate or inconspicuous prophylls of the axillary buds, biternate leaves, actinodromous venation, calyx cupulate or spathaceous, calyx apices dentate or irregularly lobed, fruits with winged valves, and fruit midrib limited by two longitudinal ridges were reconstructed as potential synapomorphies of different clades within the genus. Other traits such as habit, tertiary venation, inflorescence type, corolla color, number of ovule series, and pollen unit were highly labile. As circumscribed here, Cuspidaria is composed of eight main clades supported by molecular data and morphological synapomorphies: Sideropogon, Tetrastichella, Cinerea, Paracarpaea, Cremastus, Blepharitheca, Saldanhaea, and Cuspidaria s.str. clades. All species are monophyletic, except for C. pulchra and C. sceptrum, which form a species complex and are best treated as a single taxon. The necessary taxonomic changes are proposed, leading to the recognition of 19 species in Cuspidaria.

Using Auxiliary Information in Probability Survey Data to Improve Pseudo-Weighting in Nonprobability Samples: A Copula Model Approach.

While probability sampling has been considered the gold standard of survey methods, nonprobability sampling is increasingly popular due to its convenience and low cost. However, nonprobability samples can lead to biased estimates due to the unknown nature of the underlying selection mechanism. In this article, we propose parametric and semiparametric approaches to integrate probability and nonprobability samples using common ancillary variables observed in both samples. In the parametric approach, the joint distribution of ancillary variables is assumed to follow the latent Gaussian copula model, which is flexible to accommodate both categorical and continuous variables. In contrast, the semiparametric approach requires no assumptions about the distribution of ancillary variables. In addition, logistic regression is used to model the mechanism by which population units enter the nonprobability sample. The unknown parameters in the copula model are estimated through the pseudo maximum likelihood approach. The logistic regression model is estimated by maximizing the sample likelihood constructed from the nonprobability sample. The proposed method is evaluated in the context of estimating the population mean. Our simulation results show that the proposed method is able to correct the selection bias in the nonprobability sample by consistently estimating the underlying inclusion mechanism. By incorporating additional information in the nonprobability sample, the combined method can estimate the population mean more efficiently than using the probability sample alone. A real-data application is provided to illustrate the practical use of the proposed method.

Stochastic Optimal Control for Multivariable Dynamical Systems Using Expectation Maximization.

Trajectory optimization is a fundamental stochastic optimal control (SOC) problem. This article deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic models. Exact/complete solutions to these kind of control problems have been deemed analytically intractable in literature because they come under the category of partially observable Markov decision processes (MDPs). Therefore, effective solutions with reasonable approximations are widely sought for. We propose a reformulation of stochastic control in a reinforcement learning setting. This type of formulation assimilates the benefits of conventional optimal control procedure, with the advantages of maximum likelihood approaches. Finally, an iterative trajectory optimization paradigm called as SOC-expectation maximization (SOC-EM) is put forth. This trajectory optimization procedure exhibits better performance in terms of reduction in cumulative cost-to-go which is proven both theoretically and empirically. Furthermore, we also provide novel theoretical work which is related to uniqueness of control parameter estimates. Analysis of the control covariance matrix is presented, which handles stochasticity through efficiently balancing exploration and exploitation.

Spatial Analysis of the Semeru Eruption Disaster Area

Semeru, the most active volcano in Indonesia, erupted again in December 2021. This study aimed to map the impact of damages due to the eruption and map the incompatibility of land use with the Spatial Planning. The study was carried out through multitemporal spatial analysis to map the impact of the eruption damages, while the analysis of suitability and land use direction was carried out by overlaying land use maps with Spatial Planning maps. Sentinel-1B image data were analyzed using a maximum likelihood approach to obtain land use classification before and after the eruption. The results of the study showed that the eruption had an impact on the destruction of 1001.2 Ha of High-Density Forest, 624.9 Ha of Medium-Density Forest, 450.8 Ha of Rice Fields, 436.7 Ha of Agricultural Fields, 91 Ha of Settlements, and 3.1 Ha of Water bodies in Lumajang Regency. The results of the analysis show that in the affected area, there is a spatial plan direction of a residential area of 109.7 Ha. In addition to that, the high impact of the disaster is also due to the incompatibility of land use in the conservation area as a residential area of 515.4 Ha.

Toward a simple yet efficient cost function for the optimization of Gaussian process regression model hyperparameters

FFLUX is a novel machine-learnt force field using pre-trained Gaussian process regression (GPR) models to predict energies and multipole moments of quantum atoms in molecular dynamic simulations. At the heart of FFLUX lies the program FEREBUS, a Fortran90 and OpenMP-parallelized regression engine, which trains and validates GPR models of chemical accuracy. Training a GPR model is about finding an optimal set of model hyperparameters (θ). This time-consuming task is usually accomplished by maximizing the marginal/concentrated log-likelihood function LLy|x,θ, known as the type-II maximum likelihood approach. Unfortunately, this widespread approach can suffer from the propagation of numerical errors, especially in the noise-free regime, where the expected correlation betweenLLy|x,θ̂ [maximized value of theLLy|x,θfunction] and the models’ performance may no longer be valid. In this scenario, the LLy|x,θ function is no longer a reliable guide for model selection. While one could still rely on a pre-conditioner to improve the condition number of the covariance matrix, this choice is never unique and often comes with increased computational cost. Therefore, we have equipped FEREBUS with an alternatively simple, intuitive, viable, and less error-prone protocol called “iterative hold-out cross-validation” for the optimization of θ values. This protocol involves (1) a stratified random sampling of both training and validation sets, followed by (2) an iterative minimization of the predictive RMSE(θ) of intermediary models over a sufficiently large validation set. Its greatest asset is the assurance that the optimization process keeps reducing the generalization error of intermediary GPR models on unseen datasets, something that maximizing LLy|x,θ does not guarantee.

Integrative taxonomic revision of the Metarctia Walker, 1855 subgenus HebenaWalker, 1856, with descriptions of six new species and one new subspecies(Lepidoptera: Erebidae: Arctiinae: Syntomini)

A revision of the subgenus Hebena Walker, 1856 of the syntomine genus Metarctia Walker, 1855 is given based on integrative taxonomic analyses. Six new species (Metarctia (Hebena) manfredi sp. n., M. (H.) elleni sp. n., M. (H.) brigitta sp. n., M. (H). lukaszi sp. n., M. (H.) smithi sp. n., and M. (H.) haraldsulaki sp.n.) and one new subspecies (M. (H.) smithi transvallesiana ssp. n.) are described. Metarctia (H.) kelleni (Snellen, 1886) stat. rev. is reinstated from synonymy with M. (H.) rubra (Walker, 1856) and Metarctia (H.) subincarnata Kiriakoff, 1954 syn. n. is synonymised with M. (H.) henrardi Kiriakoff, 1953 and Metarctia cinnamomea (Wallengren, 1860) syn. n. with M. (H.) rubra (Walker, 1856). DNA barcodes were obtained for 116 specimens representing 7 taxa, and genetic analyses were performed using Maximum Likelihood and Bayesian Inference approaches; a DNA barcode tree resulting from the latter is illustrated. Pairwise distances of barcodes between taxa are provided where available. The adults and genitalia of all taxa, their habitats and distribution are illustrated in 19 colour plates and 5 distribution maps.

SINE-LOMAX DISTRIBUTION: PROPERTIES AND APPLICATIONS TO REAL DATA SETS

In this study, a novel distribution called the two-parameter Sine Lomax distribution was introduced. The distribution was developed by combining the Sine generalized family of distributions with the Lomax distribution. Various statistical properties of this new distribution were investigated, including the survival function, hazard function, quantile function, rth moment, entropy, moment generating function, and order statistics. The probability density function (PDF) plot indicated that the distribution is skewed to the right. Additionally, the hazard plot of the Sine Lomax distribution showed both monotonic increase and monotonic decrease. To estimate the parameters of the newly proposed distribution, the maximum likelihood approach was employed. A simulation study was conducted to evaluate the consistency of the estimators. The simulation results indicated that the estimators are consistent, as the bias and mean square error decrease with increasing sample sizes. The performance of the Sine Lomax distribution was compared to other extensions of Lomax distributions and the baseline distribution which is the Lomax distribution using various evaluation criteria, including the Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC). The proposed distribution demonstrated the lowest scores among the competing models, indicating its potential for accurately modeling real-world data sets. Based on the results, the proposed Sine Lomax distribution is recommended as a superior alternative to the competing models for modeling certain real-world data sets.

Counting the Unseen: Estimation of Susceptibility Proportions in Zero-Inflated Models Using a Conditional Likelihood Approach

Zero-inflated count data models are widely used in various fields such as ecology, epidemiology, and transportation, where count data with a large proportion of zeros is prevalent. Despite their widespread use, their theoretical properties have not been extensively studied. This study aims to investigate the impact of ignoring heterogeneity in event count intensity and susceptibility probability on zero-inflated count data analysis within the zero-inflated Poisson framework. To address this issue, we propose a novel conditional likelihood approach that uses positive count data only to estimate event count intensity parameters and develop a consistent estimator for estimating the average susceptibility probability. Our approach is compared with the maximum likelihood approach, and we demonstrate our findings through a comprehensive simulation study and real data analysis. The results can also be extended to zero-inflated binomial and geometric models with similar conclusions. These findings contribute to the understanding of the theoretical properties of zero-inflated count data models and provide a practical approach to handling heterogeneity in such models.

Statistical analysis of the Gompertz-Makeham model using adaptive progressively hybrid Type-II censoring and its applications in various sciences

Gompertz-Makeham (GomMak) lifetime model has been popularly utilized in explaining human mortality, actuarial tables, growth models, and others. This study focuses on the inference problem of the model parameters and some life parameters, such as the survival (or reliability) and failure rate functions of the GomMak distribution, in the presence of a sample produced from an adaptive progressively hybrid Type-II strategy. To acquire estimates of the unknown objectives, the maximum likelihood and Bayesian estimation approaches are considered. Asymptotic confidence intervals for the same unknown parameters are also estimated based on the observed Fisher information. According to the assumption of gamma intensity introductions, under squared error loss, Bayes’ estimates of various parameters cannot be explicitly expressed. To handle this issue, the Metropolis-Hastings technique is used, in turn, to evaluate the complex Bayes estimates and produce their highest-posterior density interval estimates. Comprehensive numerical examinations, in terms of four-accuracy metrics, namely: root mean squared-error, mean relative absolute-biases, interval lengths, and interval coverage-probabilities, are done to evaluate the supplied estimates. To suggest the best progressive scenario, various optimal criteria are estimated through the offered frequentist estimates. Finally, three applications from the natural sciences—engineering, chemistry, and physics—are utilized to show the utility of the presented methodologies and the possibility of adjusting research aims to real-world problems. Real-world data results stated that the GomMak model provides a useful explanation for various practical situations in the presence of such controlled data.