Bayesian Estimation of Weighted Inverse Maxwell Distribution under Different Loss Functions

In this study, the shape parameter of the weighted Inverse Maxwell distribution is estimated by employing Bayesian techniques. To produce posterior distributions, the extended Jeffery's prior and the Erlang prior are utilised. The estimators are derived from the squared error loss function, the entropy loss function, the precautionary loss function, and the Linex loss function. Furthermore, an actual data set is studied to assess the effectiveness of various estimators under distinct loss functions.

The Generalized DUS Transformed Log-Normal Distribution and Its Applications to Cancer and Heart Transplant Datasets

Many studies have underlined the importance of the log-normal distribution in the modeling of phenomena occurring in biology. With this in mind, in this article we offer a new and motivated transformed version of the log-normal distribution, primarily for use with biological data. The hazard rate function, quantile function, and several other significant aspects of the new distribution are investigated. In particular, we show that the hazard rate function has increasing, decreasing, bathtub, and upside-down bathtub shapes. The maximum likelihood and Bayesian techniques are both used to estimate unknown parameters. Based on the proposed distribution, we also present a parametric regression model and a Bayesian regression approach. As an assessment of the longstanding performance, simulation studies based on maximum likelihood and Bayesian techniques of estimation procedures are also conducted. Two real datasets are used to demonstrate the applicability of the new distribution. The efficiency of the third parameter in the new model is tested by utilizing the likelihood ratio test. Furthermore, the parametric bootstrap approach is used to determine the effectiveness of the suggested model for the datasets.

A New Two-Parameter Burr-Hatke Distribution: Properties and Bayesian and Non-Bayesian Inference with Applications

This article introduces a two-parameter flexible extension of the Burr-Hatke distribution using the inverse-power transformation. The failure rate of the new distribution can be an increasing shape, a decreasing shape, or an upside-down bathtub shape. Some of its mathematical properties are calculated. Ten estimation methods, including classical and Bayesian techniques, are discussed to estimate the model parameters. The Bayes estimators for the unknown parameters, based on the squared error, general entropy, and linear exponential loss functions, are provided. The ranking and behavior of these methods are assessed by simulation results with their partial and overall ranks. Finally, the flexibility of the proposed distribution is illustrated empirically using two real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, Fréchet, gamma, exponential, inverse log-logistic, inverse weighted Lindley, inverse Pareto, inverse Nakagami-M, and Burr-Hatke distributions.

Inequality over the business cycle: the role of distributive shocks

This paper examines how wealth and income inequality dynamics are related to fluctuations in the functional income distribution over the business cycle. In a panel estimation for OECD countries between 1970 and 2016, although inequality is, on average countercyclical and significantly associated with the capital share, one-third of the countries display a pro- or noncyclical relationship. To analyze the observed pattern, we incorporate distributive shocks into an RBC model, where agents are ex ante heterogeneous with respect to wealth and ability. We find that whether wealth and income inequality behave countercyclically or not depends on the elasticity of intertemporal substitution and the persistence of shocks. We match the model to quarterly US data using Bayesian techniques. The parameter estimates point toward a non-monotonic relationship between productivity and inequality fluctuations. On impact, inequality increases in response to TFP shocks but subsequently declines. Furthermore, TFP shocks explain 17% of inequality fluctuations.

We are what we eat, plus some per mill: Using stable isotopes to estimate diet composition in Gyps vultures over space and time.

1. Dietary studies in birds of prey involve direct observation and examination of food remains at resting and nesting sites. Although these methods accurately identify diet in raptors, they are time-consuming, resource-intensive, and associated with biases from the feeding ecology of raptors like Gyps vultures. Our study set out to estimate diet composition in Gyps vultures informed by stable isotopes that provide a good representation of assimilated diet from local systems. 2. We hypothesized that differences in Gyps vulture diet composition is a function of sampling location, and that these vultures move between Serengeti National Park and Selous Game Reserve protected areas to forage. We also, theorised that grazing ungulates are the principal items in Gyps vulture diet. 3. Through combined linear and Bayesian modelling, diet-derived from 13C in Gyps vultures consisted of grazing herbivores across sites, with those in Serengeti National Park consuming higher proportions of grazing herbivores (> 87%). 13C differences in vulture feather subsets did not indicate shifts in vulture diet and combined with blood 13C, vultures fed largely on grazers for ~159 days before they were sampled. Similarly, 15N values indicated Gyps vultures fed largely on herbivores. 34S ratios separated where vultures fed when the two sites were compared. 34S variation in vultures across sites resulted from baseline differences in plant 34S values, though it is not possible to match 34S to specific locations. 4. Our findings highlight the relevance of repeated sampling that considers tissues with varying isotopic turnover and emerging Bayesian techniques for dietary studies using stable isotopes. Findings also suggested limited vulture movement between the two local systems. However, more sampling coupled with telemetry is required to fully comprehend this observation and its implications to Gyps vulture ecology and conservation.

Type I Half Logistic Burr X-G Family: Properties, Bayesian, and Non-Bayesian Estimation under Censored Samples and Applications to COVID-19 Data

In this paper, we present a new family of continuous distributions known as the type I half logistic Burr X-G. The proposed family’s essential mathematical properties, such as quantile function (QuFu), moments (Mo), incomplete moments (InMo), mean deviation (MeD), Lorenz (Lo) and Bonferroni (Bo) curves, and entropy (En), are provided. Special models of the family are presented, including type I half logistic Burr X-Lomax, type I half logistic Burr X-Rayleigh, and type I half logistic Burr X-exponential. The maximum likelihood (MLL) and Bayesian techniques are utilized to produce parameter estimators for the recommended family using type II censored data. Monte Carlo simulation is used to evaluate the accuracy of estimates for one of the family’s special models. The COVID-19 real datasets from Italy, Canada, and Belgium are analysed to demonstrate the significance and flexibility of some new distributions from the family.

Upslope migration of snow avalanches in a warming climate

Snow is highly sensitive to atmospheric warming. However, because of the lack of sufficiently long snow avalanche time series and statistical techniques capable of accounting for the numerous biases inherent to sparse and incomplete avalanche records, the evolution of process activity in a warming climate remains little known. Filling this gap requires innovative approaches that put avalanche activity into a long-term context. Here, we combine extensive historical records and Bayesian techniques to construct a 240-y chronicle of snow avalanching in the Vosges Mountains (France). We show evidence that the transition from the late Little Ice Age to the early twentieth century (i.e., 1850 to 1920 CE) was not only characterized by local winter warming in the order of +1.35 °C but that this warming also resulted in a more than sevenfold reduction in yearly avalanche numbers, a severe shrinkage of avalanche size, and shorter avalanche seasons as well as in a reduction of the extent of avalanche-prone terrain. Using a substantial corpus of snow and climate proxy sources, we explain this abrupt shift with increasingly scarcer snow conditions with the low-to-medium elevations of the Vosges Mountains (600 to 1,200 m above sea level [a.s.l.]). As a result, avalanches migrated upslope, with only a relict activity persisting at the highest elevations (release areas >1,200 m a.s.l.). This abrupt, unambiguous response of snow avalanche activity to warming provides valuable information to anticipate likely changes in avalanche behavior in higher mountain environments under ongoing and future warming.

We are what we eat, plus some per mill: Using stable isotopes to estimate diet composition in Gyps vultures over space and time.

1. Dietary studies in birds of prey involve direct observation and examination of food remains at resting and nesting sites. Although these methods accurately identify diet in raptors, they are time-consuming, resource-intensive, and associated with biases from the feeding ecology of raptors like Gyps vultures. Our study set out to estimate diet composition in Gyps vultures informed by stable isotopes that provide a good representation of assimilated diet from local systems. 2. We hypothesized that differences in Gyps vulture diet composition is a function of sampling location, and that these vultures move between Serengeti National Park and Selous Game Reserve protected areas to forage. We also, theorised that grazing ungulates are the principal items in Gyps vulture diet. 3. Through combined linear and Bayesian modelling, diet-derived from 13C in Gyps vultures consisted of grazing herbivores across sites, with those in Serengeti National Park consuming higher proportions of grazing herbivores (> 87%). 13C differences in vulture feather subsets did not indicate shifts in vulture diet and combined with blood 13C, vultures fed largely on grazers for ~159 days before they were sampled. Similarly, 15N values indicated Gyps vultures fed largely on herbivores. 34S ratios separated where vultures fed when the two sites were compared. 34S variation in vultures across sites resulted from baseline differences in plant 34S values, though it is not possible to match 34S to specific locations. 4. Our findings highlight the relevance of repeated sampling that considers tissues with varying isotopic turnover and emerging Bayesian techniques for dietary studies using stable isotopes. Findings also suggested limited vulture movement between the two local systems. However, more sampling coupled with telemetry is required to fully comprehend this observation and its implications to Gyps vulture ecology and conservation.

Drift Estimation of Multiscale Diffusions Based on Filtered Data

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coefficient of the homogenized equation requires pre-processing of the data, often in the form of subsampling; this is because the two-scale equation and the homogenized single-scale equation are incompatible at small scales, generating mutually singular measures on the path space. We avoid subsampling and work instead with filtered data, found by application of an appropriate kernel function, and compute maximum likelihood estimators based on the filtered process. We show that the estimators we propose are asymptotically unbiased and demonstrate numerically the advantages of our method with respect to subsampling. Finally, we show how our filtered data methodology can be combined with Bayesian techniques and provide a full uncertainty quantification of the inference procedure.