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Data sets that contain an excessive number of zeros appear in several fields of applications. This chapter considers a zero-inflated Lomax distribution as a possible model for these types of data, and presents and analyzes the performance of a Shewhart control chart for process monitoring. Several approaches allow for frequent zero observations, and among them, the most common are zero-inflated models and hurdle models in case of count data, and the use of zero-inflated distributions to model semi-continuous data, that is, data from a continuous distribution with one or more than one point of mass. The chapter presents some motivation for the use of the zero-inflated Lomax distribution together with some properties of this distribution. It proposes a Shewhart-type control chart for monitoring zero-inflated Lomax data, and analyzes its performance under some scenarios.

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We propose a statistical duality among the preferences and endowments of the agents. Under this duality, the logarithmic prices of random trades among agents in a decentralized economy converge in expectation to the logarithm of the Walrasian equilibrium price in a centralized economy.

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Background/Objectives: Type 2 diabetes mellitus (T2DM) is a chronic condition marked by hyperglycemia, which can affect metabolic, vascular, and hematological parameters. A low-carbohydrate, high-fat (LCHF) diet has been shown to improve glycemic control and blood pressure regulation. Exercise in hypoxia (EH) enhances insulin sensitivity, erythropoiesis, and angiogenesis. The combination of LCHF and EH may offer a promising strategy for managing T2DM and hypertension (HTN), although evidence remains limited. This study aimed to assess the effects of an eight-week normobaric EH intervention at 3000 m simulated altitude combined with an LCHF diet on hematological and lipid profiles, inflammation, and blood pressure in older patients with T2DM and HTN. Methods: Forty-two diabetic patients with HTN were randomly assigned to three groups: (1) control group (control diet + exercise in normoxia), (2) EH group (control diet + EH), and (3) intervention group (EH+LCHF) Baseline and eight-week measurements included systolic, diastolic, and mean blood pressure (SBP, DBP, MAP), hematological and lipid profiles, and inflammation biomarkers. Results: Blood pressure decreased after the intervention (p < 0.001), with no significant differences between groups (SBP: p = 0.151; DBP: p = 0.124; MAP: p = 0.18). No differences were observed in lipid profile or C-reactive protein levels (p > 0.05). Mean corpuscular hemoglobin (MCH) increased in the EH group (p = 0.027), while it decreased in the EH+LCHF group (p = 0.046). Conclusions: Adding hypoxia or restricting carbohydrates did not provide additional benefits on blood pressure in T2DM patients with HTN. Further elucidation of the mechanisms underlying hematological adaptations is imperative.

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Introduction: Together with sociodemographic and clinical features, locus of control and self-efficacy may impact the processes underlying changes in eating habits. Objectives: To study the relationships of sociodemographic and clinical characteristics, locus of control, general self-efficacy and eating self-efficacy with the perception of adherence to healthy eating among patients undergoing treatment for overweight. Methodology: A convenience sample of 74 overweight (BMI = 25.0 kg/m2) individuals (77.0% females, mean age = 41 years, SD = 11) attending nutrition consultations was studied regarding sociodemographic and clinical data, stages of change towards healthy eating, health locus of control (Health Locus of Control Scale), eating self-efficacy (General Eating Self-Efficacy Scale) and general self-efficacy (Self-Concept Clinical Inventory’s self-efficacy factor). Results: Approximately two-thirds (67.6%) of participants were in the “Action/Maintenance” stage towards healthy eating. In the total locus of control scale, general self-efficacy and eating self-efficacy, participants showed average scores slightly higher than the midpoint of the respective scales. In a binary logistic regression model, sociodemographic, clinical, locus of control and self-efficacy variables significantly predicted being in the action/maintenance stage towards healthy eating (p < 0.001; Nagelkerkle’s R2 = 48.4%). A higher proportion of weight loss (adjusted Exp(ß) = 1.074, p = 0.017) and higher eating self-efficacy (adjusted Exp(ß) = 1.317, p = 0.005) were significantly associated with higher odds of being in the “Action/Maintenance” stage. Conclusions: Most participants attending nutrition consultations to treat overweight considered following a healthy diet. Higher eating self-efficacy and greater weight loss associated to being in the “Action/Maintenance” stage towards healthy eating.