| Summary: | We explore a unified model of dark matter and dark energy. This new model is a generalization of the generalized Chaplygin gas model and is known as a new generalized Chaplygin gas (NGCG) model. We study the evolutions of the Hubble parameter and the distance modulus for the model under consideration and the standard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM model and compare that with the observational datasets. Furthermore, we demonstrate two geometric diagnostics analyses including the statefinder <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>O</mi><mi>m</mi></msub><mrow><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> to the discriminant NGCG model from the standard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM model. The trajectories of evolution for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>O</mi><mi>m</mi></msub><mrow><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> diagnostic planes are shown to understand the geometrical behavior of the NGCG model by using different observational data points.
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