| Summary: | Statistical models are useful in explaining and forecasting real-world occurrences. Various extended distributions have been widely employed for modeling data in a variety of fields throughout the last few decades. In this article we introduce a new extension of the Kumaraswamy exponential (KE) model called the Kavya–Manoharan KE <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>K</mi><mi>M</mi><mi>K</mi><mi>E</mi><mo>)</mo></mrow></semantics></math></inline-formula> distribution. Some statistical and computational features of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mi>M</mi><mi>K</mi><mi>E</mi></mrow></semantics></math></inline-formula> distribution including the quantile (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Q</mi><mi>U</mi><mi>A</mi></mrow></semantics></math></inline-formula>) function, moments (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>O</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>s), incomplete <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>O</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>s (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>N</mi><mi>M</mi><msub><mi>O</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>s), conditional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>O</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>s (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>O</mi><mi>M</mi><msub><mi>O</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>s) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>O</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula> generating functions are computed. Classical maximum likelihood and Bayesian estimation approaches are employed to estimate the parameters of the KMKE model. The simulation experiment examines the accuracy of the model parameters by employing Bayesian and maximum likelihood estimation methods. We utilize two real datasets related to food chain data in this work to demonstrate the importance and flexibility of the proposed model. The new KMKE proposed distribution is very flexible, more so than numerous well-known distributions.
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